196:@0.054582:0.966558:0.078778:0.966558:0.078778:0.950778:0.054582:0.950778:0.000000:0.000000:0.000000 Interdisciplinariedad:@0.199644:0.575966:0.346429:0.575966:0.346429:0.560494:0.199644:0.560494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática y Salud:@0.199880:0.605016:0.329726:0.605016:0.329726:0.589544:0.199880:0.589544:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El agua necesita ser tratada para :@0.153337:0.620436:0.364132:0.620436:0.364132:0.605373:0.153337:0.605373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el consumo humano. El trata-:@0.153337:0.636278:0.345084:0.636278:0.345084:0.621215:0.153337:0.621215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 miento se hace en instalaciones :@0.153337:0.652120:0.361689:0.652120:0.361689:0.637057:0.153337:0.637057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 centralizadas que necesitan :@0.153337:0.667962:0.334388:0.667962:0.334388:0.652899:0.153337:0.652899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 controlar flujos de agua, volú-:@0.153337:0.683804:0.346208:0.683804:0.346208:0.668741:0.153337:0.668741:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 men y tiempo de circulación. :@0.153337:0.699646:0.345682:0.699646:0.345682:0.684583:0.153337:0.684583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Estos cálculos se llevan a cabo :@0.153337:0.715488:0.351593:0.715488:0.351593:0.700425:0.153337:0.700425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 por medio de la matémática y :@0.153337:0.731330:0.352595:0.731330:0.352595:0.716267:0.153337:0.716267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de sus herramientas (por ejem-:@0.153337:0.747172:0.355568:0.747172:0.355568:0.732109:0.153337:0.732109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 plo, el cálculo integral).:@0.153337:0.763014:0.301479:0.763014:0.301479:0.747951:0.153337:0.747951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Indaga escribe:@0.153344:0.896913:0.261012:0.896913:0.261012:0.881652:0.153344:0.881652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.198744:0.896715:0.213449:0.896715:0.213449:0.881652:0.198744:0.881652:0.000000:0.000000:0.000000 otras aplica-:@0.261012:0.896715:0.343613:0.896715:0.343613:0.881652:0.261012:0.881652:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ciones de las integrales en la :@0.153344:0.912557:0.338528:0.912557:0.338528:0.897494:0.153344:0.897494:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 vida diaria.:@0.153344:0.928399:0.222035:0.928399:0.222035:0.913336:0.153344:0.913336:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = ( ( – 1):@0.404236:0.103323:0.567974:0.103323:0.567974:0.086825:0.404236:0.086825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x dx:@0.423020:0.103439:0.473559:0.103439:0.473559:0.086970:0.423020:0.086970:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.432228:0.106667:0.437686:0.106667:0.437686:0.097066:0.432228:0.097066:0.000000 β:@0.515171:0.110397:0.524933:0.110397:0.524933:0.092262:0.515171:0.092262:0.000000 j:@0.530888:0.103439:0.534742:0.103439:0.534742:0.086970:0.530888:0.086970:0.000000 2 2:@0.567972:0.096970:0.587281:0.096970:0.587281:0.087352:0.567972:0.087352:0.000000:0.000000:0.000000 h h:@0.572926:0.103439:0.610920:0.103439:0.610920:0.086970:0.572926:0.086970:0.000000:0.000000:0.000000 ) = :@0.587281:0.103323:0.630012:0.103323:0.630012:0.086825:0.587281:0.086825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.630010:0.110397:0.639772:0.110397:0.639772:0.092262:0.630010:0.092262:0.000000 h:@0.639775:0.103439:0.649176:0.103439:0.649176:0.086970:0.639775:0.086970:0.000000 3:@0.649176:0.096970:0.654130:0.096970:0.654130:0.087352:0.649176:0.087352:0.000000 ( – 1):@0.654130:0.103323:0.717879:0.103323:0.717879:0.086825:0.654130:0.086825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.680793:0.103439:0.684646:0.103439:0.684646:0.086970:0.680793:0.086970:0.000000 2:@0.717878:0.096970:0.722831:0.096970:0.722831:0.087352:0.717878:0.087352:0.000000 = :@0.404236:0.138025:0.494321:0.138025:0.494321:0.121527:0.404236:0.121527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.494319:0.145099:0.504081:0.145099:0.504081:0.126963:0.494319:0.126963:0.000000 h:@0.504084:0.138140:0.513485:0.138140:0.513485:0.121672:0.504084:0.121672:0.000000 3:@0.513485:0.131672:0.518438:0.131672:0.518438:0.122053:0.513485:0.122053:0.000000 = :@0.518439:0.138025:0.737826:0.138025:0.737826:0.121527:0.518439:0.121527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.699067:0.145099:0.708829:0.145099:0.708829:0.126963:0.699067:0.126963:0.000000 = 1 – 1 – .:@0.404229:0.172726:0.658785:0.172726:0.658785:0.156228:0.404229:0.156228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.490561:0.179800:0.500324:0.179800:0.500324:0.161665:0.490561:0.161665:0.000000 Para suficientemente grande, y son suficientemente peque-:@0.404233:0.214556:0.891509:0.214556:0.891509:0.198058:0.404233:0.198058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.438718:0.214672:0.448081:0.214672:0.448081:0.198203:0.438718:0.198203:0.000000 ños. Luego,:@0.404233:0.231907:0.482814:0.231907:0.482814:0.215409:0.404233:0.215409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lím ( ) = lím 1 – 1 – = .:@0.464629:0.266608:0.831378:0.266608:0.831378:0.250110:0.464629:0.250110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x dx:@0.512677:0.266724:0.563215:0.266723:0.563215:0.250254:0.512677:0.250255:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.521885:0.269953:0.527344:0.269953:0.527344:0.260352:0.521885:0.260352:0.000000 β:@0.608967:0.273682:0.618730:0.273682:0.618730:0.255546:0.608967:0.255546:0.000000 β:@0.794006:0.273682:0.803768:0.273682:0.803768:0.255546:0.794006:0.255546:0.000000 :@0.404229:0.283958:0.408371:0.283958:0.408371:0.267461:0.404229:0.267461:0.000000 La integral definida de viene dada como::@0.404229:0.301309:0.699966:0.301309:0.699966:0.284811:0.404229:0.284811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.565978:0.301425:0.570274:0.301425:0.570274:0.284956:0.565978:0.284956:0.000000 f x dx = :@0.495507:0.336126:0.575555:0.336126:0.575555:0.319657:0.495507:0.319657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.520514:0.336011:0.539895:0.336011:0.539895:0.319513:0.520514:0.319513:0.000000:0.000000:0.000000 :@0.575555:0.336011:0.587981:0.336011:0.587981:0.319513:0.575555:0.319513:0.000000:0.000000:0.000000 β:@0.587981:0.343085:0.597744:0.343085:0.597744:0.324949:0.587981:0.324949:0.000000 x dx:@0.597746:0.336126:0.626664:0.336126:0.626664:0.319657:0.597746:0.319657:0.000000:0.000000:0.000000:0.000000 2:@0.605221:0.329659:0.610175:0.329659:0.610175:0.320041:0.605221:0.320041:0.000000 = lím ( ):@0.626664:0.336011:0.727465:0.336011:0.727465:0.319513:0.626664:0.319513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x dx =:@0.693419:0.336126:0.758981:0.336126:0.758981:0.319657:0.693419:0.319657:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.702627:0.339356:0.708085:0.339356:0.708085:0.329755:0.702627:0.329755:0.000000 .:@0.758983:0.336011:0.800498:0.336011:0.800498:0.319513:0.758983:0.319513:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.763124:0.343085:0.772887:0.343085:0.772887:0.324949:0.763124:0.324949:0.000000 :@0.404231:0.353361:0.408373:0.353361:0.408373:0.336864:0.404231:0.336864:0.000000 f x dx = :@0.521306:0.388178:0.597211:0.388178:0.597211:0.371710:0.521306:0.371710:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.542170:0.388063:0.561551:0.388063:0.561551:0.371565:0.542170:0.371565:0.000000:0.000000:0.000000 :@0.597211:0.388063:0.609637:0.388063:0.609637:0.371565:0.597211:0.371565:0.000000:0.000000:0.000000 β:@0.609637:0.395137:0.619400:0.395137:0.619400:0.377001:0.609637:0.377001:0.000000 x dx:@0.619402:0.388178:0.648322:0.388178:0.648322:0.371710:0.619402:0.371710:0.000000:0.000000:0.000000:0.000000 2:@0.626877:0.381711:0.631830:0.381711:0.631830:0.372093:0.626877:0.372093:0.000000 = = .:@0.648322:0.388063:0.774700:0.388063:0.774700:0.371565:0.648322:0.371565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.670013:0.395137:0.679775:0.395137:0.679775:0.377001:0.670013:0.377001:0.000000 |:@0.704630:0.388800:0.709639:0.388800:0.709639:0.369003:0.704630:0.369003:0.000000 b:@0.757725:0.388178:0.766992:0.388178:0.766992:0.371710:0.757725:0.371710:0.000000 3:@0.766991:0.381711:0.771944:0.381711:0.771944:0.372093:0.766991:0.372093:0.000000 :@0.404229:0.405414:0.408371:0.405414:0.408371:0.388916:0.404229:0.388916:0.000000 Por otro lado, a la integral indefinida de la función la designamos con :@0.404229:0.422764:0.895972:0.422764:0.895972:0.406267:0.404229:0.406267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.754625:0.422880:0.758921:0.422880:0.758921:0.406411:0.754625:0.406411:0.000000 F x:@0.404229:0.449137:0.425209:0.449137:0.425209:0.432669:0.404229:0.432669:0.000000:0.000000:0.000000 ( ) = + , , siendo . Resulta así que::@0.411781:0.449022:0.798138:0.449026:0.798138:0.432528:0.411781:0.432524:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.470963:0.449137:0.478438:0.449137:0.478438:0.432669:0.470963:0.432669:0.000000 3:@0.478444:0.442673:0.483397:0.442673:0.483397:0.433054:0.478444:0.433054:0.000000 k:@0.502490:0.449141:0.510735:0.449141:0.510735:0.432672:0.502490:0.432672:0.000000 ∀:@0.525916:0.456612:0.537488:0.456612:0.537488:0.437613:0.525916:0.437613:0.000000 x:@0.537495:0.449141:0.544970:0.449141:0.544970:0.432672:0.537495:0.432672:0.000000 :@0.549111:0.448507:0.563763:0.448507:0.563763:0.435134:0.549111:0.435134:0.000000 :@0.567905:0.447939:0.581210:0.447939:0.581210:0.435076:0.567905:0.435076:0.000000 k:@0.639158:0.449141:0.647404:0.449141:0.647404:0.432672:0.639158:0.432672:0.000000 :@0.651547:0.448507:0.666199:0.448507:0.666199:0.435134:0.651547:0.435134:0.000000 :@0.670341:0.447939:0.683646:0.447939:0.683646:0.435076:0.670341:0.435076:0.000000 F b:@0.449360:0.483843:0.472131:0.483843:0.472131:0.467374:0.449360:0.467374:0.000000:0.000000:0.000000 ( ) = (0) = + – × 0 + = = .:@0.456912:0.483727:0.846648:0.483727:0.846648:0.467229:0.456912:0.467229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F:@0.497176:0.483843:0.504728:0.483843:0.504728:0.467374:0.497176:0.467374:0.000000 b:@0.564932:0.483843:0.574198:0.483843:0.574198:0.467374:0.564932:0.467374:0.000000 3:@0.574196:0.477374:0.579149:0.477374:0.579149:0.467756:0.574196:0.467756:0.000000 k:@0.598240:0.483843:0.606485:0.483843:0.606485:0.467374:0.598240:0.467374:0.000000 3:@0.673566:0.477374:0.678519:0.477374:0.678519:0.467756:0.673566:0.467756:0.000000 k:@0.697612:0.483843:0.705857:0.483843:0.705857:0.467374:0.697612:0.467374:0.000000 b:@0.753943:0.483843:0.763210:0.483843:0.763210:0.467374:0.753943:0.467374:0.000000 3:@0.763208:0.477374:0.768161:0.477374:0.768161:0.467756:0.763208:0.467756:0.000000 x:@0.812104:0.483843:0.819579:0.483843:0.819579:0.467374:0.812104:0.467374:0.000000 3:@0.819578:0.477374:0.824532:0.477374:0.824532:0.467756:0.819578:0.467756:0.000000 |:@0.828673:0.484464:0.833682:0.484464:0.833682:0.464667:0.828673:0.464667:0.000000 Conclusión:@0.404240:0.521913:0.490722:0.521913:0.490722:0.504967:0.404240:0.504967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.404240:0.551626:0.420808:0.551626:0.420808:0.535129:0.404240:0.535129:0.000000:0.000000:0.000000:0.000000 β:@0.420804:0.558695:0.430567:0.558695:0.430567:0.540560:0.420804:0.540560:0.000000 x dx:@0.430569:0.551737:0.459489:0.551737:0.459489:0.535268:0.430569:0.535268:0.000000:0.000000:0.000000:0.000000 2:@0.438044:0.545268:0.442997:0.545268:0.442997:0.535650:0.438044:0.535650:0.000000 = = . De manera general, se prueba que: :@0.459489:0.551621:0.836988:0.551621:0.836988:0.535124:0.459489:0.535124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.500736:0.551737:0.508211:0.551737:0.508211:0.535268:0.500736:0.535268:0.000000 3:@0.508208:0.545268:0.513161:0.545268:0.513161:0.535650:0.508208:0.535650:0.000000 |:@0.517303:0.552359:0.522312:0.552359:0.522312:0.532562:0.517303:0.532562:0.000000 b:@0.568183:0.551737:0.577449:0.551737:0.577449:0.535268:0.568183:0.535268:0.000000 3:@0.577449:0.545268:0.582402:0.545268:0.582402:0.535650:0.577449:0.535650:0.000000 :@0.514780:0.593451:0.531348:0.593451:0.531348:0.576953:0.514780:0.576953:0.000000:0.000000:0.000000:0.000000 β:@0.531352:0.600525:0.541114:0.600525:0.541114:0.582389:0.531352:0.582389:0.000000 x dx:@0.541117:0.593566:0.573571:0.593566:0.573571:0.577097:0.541117:0.577097:0.000000:0.000000:0.000000:0.000000 m:@0.548476:0.587165:0.557102:0.587165:0.557102:0.577564:0.548476:0.577564:0.000000 = :@0.573571:0.593450:0.639092:0.593450:0.639092:0.576953:0.573571:0.576953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.638129:0.593566:0.645604:0.593566:0.645604:0.577097:0.638129:0.577097:0.000000 m:@0.645486:0.587165:0.654112:0.587165:0.654112:0.577564:0.645486:0.577564:0.000000 +1:@0.654112:0.587097:0.665366:0.587097:0.665366:0.577479:0.654112:0.577479:0.000000:0.000000 = :@0.665366:0.593450:0.749381:0.593450:0.749381:0.576953:0.665366:0.576953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 |:@0.669507:0.594188:0.674516:0.594188:0.674516:0.574391:0.669507:0.574391:0.000000 b:@0.749381:0.593566:0.758647:0.593566:0.758647:0.577097:0.749381:0.577097:0.000000 m:@0.758588:0.587165:0.767214:0.587165:0.767214:0.577564:0.758588:0.577564:0.000000 +1:@0.767214:0.587097:0.778468:0.587097:0.778468:0.577479:0.767214:0.577479:0.000000:0.000000 .:@0.778468:0.593450:0.781223:0.593450:0.781223:0.576953:0.778468:0.576953:0.000000 Otra propiedad de las integrales definidas:@0.404236:0.636677:0.739484:0.636677:0.739484:0.618994:0.404236:0.618994:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea una función real definida en el intervalo [ , ]. Se supone que: :@0.404236:0.653385:0.895922:0.653385:0.895922:0.636887:0.404236:0.636887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.433558:0.653500:0.437854:0.653500:0.437854:0.637032:0.433558:0.637032:0.000000 a b:@0.742261:0.653500:0.768465:0.653500:0.768465:0.637032:0.742261:0.637032:0.000000:0.000000:0.000000 f x:@0.404236:0.670851:0.421960:0.670851:0.421960:0.654382:0.404236:0.654382:0.000000:0.000000:0.000000 ( ) ≥ 0, [ , ],:@0.408532:0.670736:0.551800:0.670736:0.551800:0.654238:0.408532:0.654238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.470680:0.678322:0.482252:0.678322:0.482252:0.659323:0.470680:0.659323:0.000000 x:@0.482260:0.670851:0.489735:0.670851:0.489735:0.654382:0.482260:0.654382:0.000000 :@0.493877:0.670217:0.508529:0.670217:0.508529:0.656844:0.493877:0.656844:0.000000 a b:@0.518529:0.670851:0.543381:0.670851:0.543381:0.654382:0.518529:0.654382:0.000000:0.000000:0.000000 S:@0.505332:0.688202:0.513211:0.688202:0.513211:0.671733:0.505332:0.671733:0.000000 = {( , ) :@0.513115:0.688086:0.593893:0.688086:0.593893:0.671589:0.513115:0.671589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x y:@0.543535:0.688202:0.565305:0.688202:0.565305:0.671733:0.543535:0.671733:0.000000:0.000000:0.000000 :@0.575097:0.687568:0.589750:0.687568:0.589750:0.674194:0.575097:0.674194:0.000000 :@0.593892:0.686999:0.607196:0.686999:0.607196:0.674137:0.593892:0.674137:0.000000 2 :@0.607196:0.681734:0.614508:0.681734:0.614508:0.672116:0.607196:0.672116:0.000000:0.000000 | 0 ≤ ≤ ( ), ≤ ≤ },:@0.614452:0.688086:0.790691:0.688086:0.790691:0.671589:0.614452:0.671589:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y f x:@0.654659:0.688202:0.698583:0.688202:0.698583:0.671733:0.654659:0.671733:0.000000:0.000000:0.000000:0.000000:0.000000 a x b:@0.719139:0.688202:0.782272:0.688202:0.782272:0.671733:0.719139:0.671733:0.000000:0.000000:0.000000:0.000000:0.000000 y que es una primitiva de . Entonces, el área de la región es::@0.404249:0.712565:0.846941:0.712565:0.846941:0.696068:0.404249:0.696068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F:@0.447364:0.712681:0.454916:0.712681:0.454916:0.696212:0.447364:0.696212:0.000000 f:@0.598248:0.712681:0.602544:0.712681:0.602544:0.696212:0.598248:0.696212:0.000000 S:@0.817504:0.712681:0.825383:0.712681:0.825383:0.696212:0.817504:0.696212:0.000000 a S:@0.562089:0.738938:0.584899:0.738938:0.584899:0.722470:0.562089:0.722470:0.000000:0.000000:0.000000 ( ) = ( ):@0.571067:0.738823:0.650189:0.738823:0.650189:0.722325:0.571067:0.722325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x dx = F x:@0.614086:0.738938:0.706829:0.738938:0.706829:0.722470:0.614086:0.722470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) .:@0.693401:0.738823:0.733924:0.738826:0.733924:0.722328:0.693401:0.722325:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 |:@0.716913:0.739563:0.721922:0.739563:0.721922:0.719766:0.716913:0.719766:0.000000 Integrales definidas de funciones polinomiales:@0.404236:0.774925:0.774923:0.774925:0.774923:0.757242:0.404236:0.757242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Los resultados obtenidos en la sección precedente se extienden a :@0.404236:0.791633:0.895880:0.791633:0.895880:0.775135:0.404236:0.775135:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cualquier intervalo cerrado [ , ]. Sea una función real definida en :@0.404236:0.808983:0.895864:0.808983:0.895864:0.792486:0.404236:0.792486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.608581:0.809099:0.634938:0.809099:0.634938:0.792630:0.608581:0.792630:0.000000:0.000000:0.000000 f:@0.678304:0.809099:0.682600:0.809099:0.682600:0.792630:0.678304:0.792630:0.000000 el intervalo ] , [ y una primitiva de . De la definición de primitiva :@0.404236:0.826334:0.895903:0.826334:0.895903:0.809836:0.404236:0.809836:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.493588:0.826450:0.519134:0.826450:0.519134:0.809981:0.493588:0.809981:0.000000:0.000000:0.000000 P:@0.541906:0.826450:0.550691:0.826450:0.550691:0.809981:0.541906:0.809981:0.000000 f:@0.677129:0.826450:0.681425:0.826450:0.681425:0.809981:0.677129:0.809981:0.000000 de , se tiene::@0.404236:0.843685:0.494455:0.843685:0.494455:0.827187:0.404236:0.827187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.426237:0.843800:0.430533:0.843800:0.430533:0.827332:0.426237:0.827332:0.000000 ( ) = ( ), ] , [.:@0.556104:0.868164:0.739895:0.868163:0.739895:0.851666:0.556104:0.851666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.586909:0.868279:0.594384:0.868279:0.594384:0.851811:0.586909:0.851811:0.000000 f x:@0.619429:0.868279:0.637153:0.868279:0.637153:0.851811:0.619429:0.851811:0.000000:0.000000:0.000000 ∀:@0.658295:0.875750:0.669867:0.875750:0.669867:0.856751:0.658295:0.856751:0.000000 x:@0.669874:0.868279:0.677349:0.868279:0.677349:0.851810:0.669874:0.851810:0.000000 :@0.681490:0.867645:0.696143:0.867645:0.696143:0.854271:0.681490:0.854271:0.000000 a b:@0.706142:0.868279:0.731283:0.868279:0.731283:0.851810:0.706142:0.851810:0.000000:0.000000:0.000000 Por otro lado, ( ) = + ( ):@0.404236:0.902865:0.615268:0.902865:0.615268:0.886367:0.404236:0.886367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P x:@0.504570:0.902980:0.526782:0.902980:0.526782:0.886512:0.504570:0.886512:0.000000:0.000000:0.000000 k:@0.551827:0.902980:0.560073:0.902980:0.560073:0.886512:0.551827:0.886512:0.000000 f x dx k:@0.591591:0.902980:0.659096:0.902980:0.659096:0.886512:0.591591:0.886512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = + ( ):@0.635901:0.902865:0.730705:0.902865:0.730705:0.886367:0.635901:0.886367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x dx.:@0.717277:0.902980:0.750163:0.902980:0.750163:0.886512:0.717277:0.886512:0.000000:0.000000:0.000000:0.000000:0.000000 Escribimos ( ) = ( ) + ( ) , , ].:@0.404236:0.937566:0.725278:0.937567:0.725278:0.921069:0.404236:0.921069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P x:@0.485168:0.937682:0.507380:0.937682:0.507380:0.921213:0.485168:0.921213:0.000000:0.000000:0.000000 P a:@0.532425:0.937682:0.556141:0.937682:0.556141:0.921213:0.532425:0.921213:0.000000:0.000000:0.000000 f t dt:@0.597754:0.937682:0.634358:0.937682:0.634358:0.921213:0.597754:0.921213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ∀:@0.649535:0.945153:0.661107:0.945153:0.661107:0.926154:0.649535:0.926154:0.000000 x:@0.661114:0.937683:0.668589:0.937683:0.668589:0.921214:0.661114:0.921214:0.000000 :@0.672732:0.937048:0.687384:0.937048:0.687384:0.923675:0.672732:0.923675:0.000000 a b:@0.691526:0.937683:0.716667:0.937683:0.716667:0.921214:0.691526:0.921214:0.000000:0.000000:0.000000 ∫:@0.407410:0.107340:0.414433:0.107340:0.416872:0.081156:0.409849:0.081156:0.000000 b:@0.418194:0.087955:0.423597:0.087955:0.423597:0.078354:0.418194:0.078354:0.000000 0:@0.414769:0.109568:0.419722:0.109568:0.419722:0.099950:0.414769:0.099950:0.000000 ∑:@0.492310:0.104604:0.507689:0.104604:0.507689:0.078781:0.492310:0.078781:0.000000 n:@0.497745:0.085237:0.503203:0.085237:0.503203:0.075635:0.497745:0.075635:0.000000 j:@0.493724:0.110298:0.495970:0.110298:0.495970:0.100696:0.493724:0.100696:0.000000 =1:@0.495970:0.110230:0.507224:0.110230:0.507224:0.100612:0.495970:0.100612:0.000000:0.000000 ∑:@0.658159:0.104604:0.673538:0.104604:0.673538:0.078781:0.658159:0.078781:0.000000 n:@0.663593:0.085237:0.669052:0.085237:0.669052:0.075635:0.663593:0.075635:0.000000 j:@0.659573:0.110298:0.661819:0.110298:0.661819:0.100696:0.659573:0.100696:0.000000 =1:@0.661819:0.110230:0.673073:0.110230:0.673073:0.100612:0.661819:0.100612:0.000000:0.000000 ( – 1) (1 + 2( – 1)):@0.523766:0.130588:0.678216:0.130588:0.678216:0.114090:0.523766:0.114090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.529719:0.130703:0.539082:0.130703:0.539082:0.114235:0.529719:0.114235:0.000000 n:@0.572315:0.130703:0.581678:0.130703:0.581678:0.114235:0.572315:0.114235:0.000000 n:@0.629667:0.130703:0.639030:0.130703:0.639030:0.114235:0.629667:0.114235:0.000000 6:@0.596743:0.146926:0.605239:0.146926:0.605239:0.130429:0.596743:0.130429:0.000000 ( – 1) (2 – 1)):@0.747774:0.130588:0.868683:0.130588:0.868683:0.114090:0.747774:0.114090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.753727:0.130703:0.763090:0.130703:0.763090:0.114235:0.753727:0.114235:0.000000 n n:@0.796323:0.130703:0.829497:0.130703:0.829497:0.114235:0.796323:0.114235:0.000000:0.000000:0.000000 6:@0.803971:0.146926:0.812467:0.146926:0.812467:0.130429:0.803971:0.130429:0.000000 b:@0.720892:0.130653:0.730158:0.130653:0.730158:0.114184:0.720892:0.114184:0.000000 3:@0.721277:0.146876:0.729773:0.146876:0.729773:0.130378:0.721277:0.130378:0.000000 b:@0.505632:0.165453:0.514898:0.165453:0.514898:0.148984:0.505632:0.148984:0.000000 3:@0.514899:0.158984:0.519852:0.158984:0.519852:0.149366:0.514899:0.149366:0.000000 3:@0.508495:0.181682:0.516991:0.181682:0.516991:0.165184:0.508495:0.165184:0.000000 1:@0.569159:0.165337:0.577654:0.165337:0.577654:0.148839:0.569159:0.148839:0.000000 n:@0.568735:0.181791:0.578098:0.181791:0.578098:0.165323:0.568735:0.165323:0.000000 1:@0.632818:0.207005:0.641314:0.207005:0.641314:0.190508:0.632818:0.190508:0.000000 n:@0.632394:0.223459:0.641757:0.223459:0.641757:0.206991:0.632394:0.206991:0.000000 1:@0.626817:0.165337:0.635313:0.165337:0.635313:0.148839:0.626817:0.148839:0.000000 2:@0.622135:0.181676:0.630631:0.181676:0.630631:0.165178:0.622135:0.165178:0.000000 n:@0.630631:0.181791:0.639994:0.181791:0.639994:0.165323:0.630631:0.165323:0.000000 1:@0.672048:0.207005:0.680544:0.207005:0.680544:0.190508:0.672048:0.190508:0.000000 2:@0.667367:0.223344:0.675863:0.223344:0.675863:0.206846:0.667367:0.206846:0.000000 n:@0.675863:0.223459:0.685226:0.223459:0.685226:0.206991:0.675863:0.206991:0.000000 b:@0.625524:0.259037:0.634790:0.259037:0.634790:0.242569:0.625524:0.242569:0.000000 3:@0.634791:0.252569:0.639744:0.252569:0.639744:0.242951:0.634791:0.242951:0.000000 3:@0.628387:0.275267:0.636883:0.275267:0.636883:0.258769:0.628387:0.258769:0.000000 1:@0.689050:0.258922:0.697546:0.258922:0.697546:0.242424:0.689050:0.242424:0.000000 n:@0.688627:0.275376:0.697989:0.275376:0.697989:0.258907:0.688627:0.258907:0.000000 1:@0.746707:0.258922:0.755203:0.258922:0.755203:0.242424:0.746707:0.242424:0.000000 2:@0.742026:0.275260:0.750522:0.275260:0.750522:0.258763:0.742026:0.258763:0.000000 n:@0.750522:0.275376:0.759885:0.275376:0.759885:0.258907:0.750522:0.258907:0.000000 3:@0.737580:0.123998:0.742534:0.123998:0.742534:0.114380:0.737580:0.114380:0.000000 n:@0.464990:0.273443:0.471097:0.273443:0.471097:0.262703:0.464990:0.262703:0.000000 →:@0.471097:0.272761:0.481844:0.272761:0.481844:0.262750:0.471097:0.262750:0.000000 ∞:@0.481843:0.273368:0.490525:0.273368:0.490525:0.262609:0.481843:0.262609:0.000000 n:@0.582257:0.273443:0.588363:0.273443:0.588363:0.262703:0.582257:0.262703:0.000000 →:@0.588363:0.272761:0.599111:0.272761:0.599111:0.262750:0.588363:0.262750:0.000000 ∞:@0.599110:0.273368:0.607792:0.273368:0.607792:0.262609:0.599110:0.262609:0.000000 n:@0.648915:0.343884:0.655021:0.343884:0.655021:0.333143:0.648915:0.333143:0.000000 →:@0.655018:0.343200:0.665765:0.343200:0.665765:0.333189:0.655018:0.333189:0.000000 ∞:@0.665763:0.343807:0.674445:0.343807:0.674445:0.333048:0.665763:0.333048:0.000000 ∫:@0.497310:0.269877:0.504333:0.269877:0.506772:0.243694:0.499749:0.243694:0.000000 b:@0.508093:0.250492:0.513495:0.250492:0.513495:0.240891:0.508093:0.240891:0.000000 0:@0.504667:0.272106:0.509620:0.272106:0.509620:0.262488:0.504667:0.262488:0.000000 ∫:@0.498035:0.340643:0.505058:0.340643:0.507498:0.314460:0.500475:0.314460:0.000000 b:@0.508818:0.321257:0.514221:0.321257:0.514221:0.311656:0.508818:0.311656:0.000000 0:@0.505392:0.342871:0.510346:0.342871:0.510346:0.333252:0.505392:0.333252:0.000000 ∫:@0.523164:0.392192:0.530187:0.392192:0.532626:0.366009:0.525603:0.366009:0.000000 b:@0.533947:0.372806:0.539349:0.372806:0.539349:0.363205:0.533947:0.363205:0.000000 0:@0.530521:0.394420:0.535474:0.394420:0.535474:0.384802:0.530521:0.384802:0.000000 ∫:@0.407572:0.555262:0.414595:0.555262:0.417035:0.529079:0.410012:0.529079:0.000000 b:@0.418355:0.535877:0.423758:0.535877:0.423758:0.526276:0.418355:0.526276:0.000000 0:@0.414929:0.557491:0.419883:0.557491:0.419883:0.547872:0.414929:0.547872:0.000000 ∫:@0.518138:0.596931:0.525161:0.596931:0.527601:0.570748:0.520578:0.570748:0.000000 b:@0.528921:0.577547:0.534323:0.577547:0.534323:0.567945:0.528921:0.567945:0.000000 0:@0.525495:0.599160:0.530448:0.599160:0.530448:0.589542:0.525495:0.589542:0.000000 ∫:@0.596875:0.392192:0.603897:0.392192:0.606337:0.366009:0.599314:0.366009:0.000000 b:@0.607657:0.372806:0.613060:0.372806:0.613060:0.363205:0.607657:0.363205:0.000000 0:@0.604231:0.394420:0.609185:0.394420:0.609185:0.384802:0.604231:0.384802:0.000000 ∫:@0.576772:0.340643:0.583795:0.340643:0.586234:0.314460:0.579211:0.314460:0.000000 b:@0.587554:0.321257:0.592957:0.321257:0.592957:0.311656:0.587554:0.311656:0.000000 0:@0.584129:0.342871:0.589082:0.342871:0.589082:0.333252:0.584129:0.333252:0.000000 ∫:@0.680636:0.340643:0.687659:0.340643:0.690099:0.314460:0.683076:0.314460:0.000000 b:@0.691419:0.321257:0.696822:0.321257:0.696822:0.311656:0.691419:0.311656:0.000000 0:@0.687993:0.342871:0.692947:0.342871:0.692947:0.333252:0.687993:0.333252:0.000000 b:@0.809800:0.259037:0.819067:0.259037:0.819067:0.242569:0.809800:0.242569:0.000000 3:@0.819067:0.252569:0.824021:0.252569:0.824021:0.242951:0.819067:0.242951:0.000000 3:@0.812661:0.275267:0.821157:0.275267:0.821157:0.258769:0.812661:0.258769:0.000000 b:@0.779567:0.329050:0.788834:0.329050:0.788834:0.312581:0.779567:0.312581:0.000000 3:@0.788833:0.322581:0.793786:0.322581:0.793786:0.312963:0.788833:0.312963:0.000000 3:@0.782428:0.345279:0.790924:0.345279:0.790924:0.328782:0.782428:0.328782:0.000000 β:@0.741093:0.388088:0.751321:0.388088:0.751321:0.369089:0.741093:0.369089:0.000000 3:@0.741961:0.396846:0.750457:0.396846:0.750457:0.380349:0.741961:0.380349:0.000000 x:@0.684918:0.380617:0.692392:0.380617:0.692392:0.364148:0.684918:0.364148:0.000000 3:@0.692392:0.374150:0.697346:0.374150:0.697346:0.364532:0.692392:0.364532:0.000000 3:@0.686883:0.396846:0.695379:0.396846:0.695379:0.380349:0.686883:0.380349:0.000000 b:@0.711651:0.379063:0.717054:0.379063:0.717054:0.369462:0.711651:0.369462:0.000000 0:@0.711876:0.390468:0.716829:0.390468:0.716829:0.380850:0.711876:0.380850:0.000000 β:@0.454111:0.448925:0.464339:0.448925:0.464339:0.429926:0.454111:0.429926:0.000000 3:@0.454979:0.457683:0.463475:0.457683:0.463475:0.441186:0.454979:0.441186:0.000000 β:@0.548493:0.483663:0.558720:0.483663:0.558720:0.464664:0.548493:0.464664:0.000000 3:@0.549359:0.492421:0.557855:0.492421:0.557855:0.475924:0.549359:0.475924:0.000000 β:@0.481984:0.551747:0.492211:0.551747:0.492211:0.532748:0.481984:0.532748:0.000000 3:@0.482852:0.560505:0.491348:0.560505:0.491348:0.544008:0.482852:0.544008:0.000000 β:@0.607640:0.593550:0.617868:0.593550:0.617868:0.574551:0.607640:0.574551:0.000000 m:@0.592573:0.602424:0.607369:0.602424:0.607369:0.585955:0.592573:0.585955:0.000000 + 1:@0.607369:0.602308:0.632953:0.602308:0.632953:0.585810:0.607369:0.585810:0.000000:0.000000:0.000000:0.000000 β:@0.719881:0.593550:0.730109:0.593550:0.730109:0.574551:0.719881:0.574551:0.000000 m:@0.704814:0.602424:0.719610:0.602424:0.719610:0.585955:0.704814:0.585955:0.000000 + 1:@0.719610:0.602308:0.745194:0.602308:0.745194:0.585810:0.719610:0.585810:0.000000:0.000000:0.000000:0.000000 β:@0.552225:0.551747:0.562453:0.551747:0.562453:0.532748:0.552225:0.532748:0.000000 3:@0.553093:0.560505:0.561589:0.560505:0.561589:0.544008:0.553093:0.544008:0.000000 β:@0.632255:0.483663:0.642482:0.483663:0.642482:0.464664:0.632255:0.464664:0.000000 3:@0.633121:0.492421:0.641617:0.492421:0.641617:0.475924:0.633121:0.475924:0.000000 β:@0.738651:0.483663:0.748878:0.483663:0.748878:0.464664:0.738651:0.464664:0.000000 3:@0.739519:0.492421:0.748015:0.492421:0.748015:0.475924:0.739519:0.475924:0.000000 β:@0.793934:0.483663:0.804161:0.483663:0.804161:0.464664:0.793934:0.464664:0.000000 3:@0.794802:0.492421:0.803298:0.492421:0.803298:0.475924:0.794802:0.475924:0.000000 b:@0.835615:0.474662:0.841018:0.474662:0.841018:0.465060:0.835615:0.465060:0.000000 0:@0.835840:0.486067:0.840793:0.486067:0.840793:0.476449:0.835840:0.476449:0.000000 b:@0.524712:0.542747:0.530115:0.542747:0.530115:0.533146:0.524712:0.533146:0.000000 0:@0.524937:0.554153:0.529890:0.554153:0.529890:0.544534:0.524937:0.544534:0.000000 b:@0.677182:0.584550:0.682584:0.584550:0.682584:0.574948:0.677182:0.574948:0.000000 0:@0.677406:0.595955:0.682360:0.595955:0.682360:0.586337:0.677406:0.586337:0.000000 ∫:@0.609394:0.742145:0.616417:0.742145:0.618856:0.715961:0.611833:0.715961:0.000000 b:@0.620178:0.722759:0.625580:0.722759:0.625580:0.713157:0.620178:0.713157:0.000000 a:@0.616606:0.744439:0.621840:0.744439:0.621840:0.734838:0.616606:0.734838:0.000000 b:@0.723240:0.729359:0.728642:0.729359:0.728642:0.719758:0.723240:0.719758:0.000000 a:@0.723329:0.740832:0.728563:0.740832:0.728563:0.731230:0.723329:0.731230:0.000000 dP:@0.559224:0.861047:0.577180:0.861047:0.577180:0.844578:0.559224:0.844578:0.000000:0.000000 dx:@0.559956:0.877385:0.576447:0.877385:0.576447:0.860917:0.559956:0.860917:0.000000:0.000000 dP:@0.687948:0.895912:0.705903:0.895912:0.705903:0.879443:0.687948:0.879443:0.000000:0.000000 dx:@0.688680:0.912250:0.705171:0.912250:0.705171:0.895782:0.688680:0.895782:0.000000:0.000000 ∫:@0.579959:0.905542:0.586371:0.905542:0.588598:0.881636:0.582186:0.881636:0.000000 ∫:@0.675436:0.905542:0.681848:0.905542:0.684075:0.881636:0.677663:0.881636:0.000000 ∫:@0.582062:0.941953:0.589085:0.941953:0.591524:0.915770:0.584502:0.915770:0.000000 x:@0.593367:0.922568:0.597725:0.922568:0.597725:0.912967:0.593367:0.912967:0.000000 a:@0.589279:0.944249:0.594513:0.944249:0.594513:0.934648:0.589279:0.934648:0.000000 Shutterstock, 373973119:@0.386147:0.882932:0.386147:0.814759:0.374678:0.814759:0.374678:0.882932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interculturalidad:@0.199644:0.107453:0.319958:0.107453:0.319958:0.091981:0.199644:0.091981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Con respecto al cálculo :@0.193071:0.136642:0.347870:0.136642:0.347870:0.121578:0.193071:0.121578:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de áreas, sabemos que el cálcu-:@0.153335:0.152484:0.355039:0.152484:0.355039:0.137420:0.153335:0.137420:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 lo de algunas de ellas es sencillo :@0.153335:0.168326:0.360617:0.168326:0.360617:0.153262:0.153335:0.153262:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (por ejemplo, cuando en geo-:@0.153335:0.184168:0.345295:0.184168:0.345295:0.169104:0.153335:0.169104:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 metría nos referimos al cálculo :@0.153335:0.200010:0.353975:0.200010:0.353975:0.184946:0.153335:0.184946:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de cuadrados, rectángulos, :@0.153335:0.215852:0.329106:0.215852:0.329106:0.200788:0.153335:0.200788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 triángulos, círculos, etc). Otras :@0.153335:0.231694:0.350543:0.231694:0.350543:0.216630:0.153335:0.216630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 áreas son más complejas, y se :@0.153335:0.247536:0.346346:0.247536:0.346346:0.232472:0.153335:0.232472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dividen en un número finito de :@0.153335:0.263378:0.359057:0.263378:0.359057:0.248314:0.153335:0.248314:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 triángulos.:@0.153335:0.279220:0.220230:0.279220:0.220230:0.264156:0.153335:0.264156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Los antiguos griegos fueron :@0.153335:0.302190:0.333902:0.302190:0.333902:0.287127:0.153335:0.287127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 capaces de encontrar fórmulas :@0.153335:0.318032:0.355108:0.318032:0.355108:0.302969:0.153335:0.302969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 para calcular áreas de regiones :@0.153335:0.333874:0.352213:0.333874:0.352213:0.318811:0.153335:0.318811:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (principalmente limitadas por :@0.153335:0.349716:0.348579:0.349716:0.348579:0.334653:0.153335:0.334653:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cónicas) mediante el método :@0.153335:0.365558:0.345713:0.365558:0.345713:0.350495:0.153335:0.350495:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de “exhaución” (Arquímedes, :@0.153335:0.381400:0.343974:0.381400:0.343974:0.366337:0.153335:0.366337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 287-212 a. C.). En esencia, se :@0.153335:0.397242:0.333527:0.397242:0.333527:0.382179:0.153335:0.382179:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 trata de un proceso al límite, :@0.153335:0.413084:0.341245:0.413084:0.341245:0.398021:0.153335:0.398021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 donde la región en estudio :@0.153335:0.428926:0.330134:0.428926:0.330134:0.413863:0.153335:0.413863:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 queda encajada entre dos :@0.153335:0.444768:0.322902:0.444768:0.322902:0.429705:0.153335:0.429705:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 polígonos, uno inscrito y el otro :@0.153335:0.460610:0.361935:0.460610:0.361935:0.445547:0.153335:0.445547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 circunscrito, cuyas áreas res-:@0.153335:0.476452:0.334301:0.476452:0.334301:0.461389:0.153335:0.461389:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pectivas se pueden calcular (no :@0.153335:0.492294:0.359537:0.492294:0.359537:0.477231:0.153335:0.477231:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 muy fácilmente, valga decirlo).:@0.153335:0.508136:0.347513:0.508136:0.347513:0.493073:0.153335:0.493073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000