227:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000 Pensamiento métrico y variacional:@0.619822:0.043660:0.926913:0.043660:0.926913:0.024915:0.619822:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b. :@0.104633:0.154705:0.121531:0.154705:0.121531:0.138992:0.104633:0.138992:0.000000:0.000000:0.000000 Observen:@0.134834:0.154705:0.207929:0.154705:0.207929:0.138035:0.134834:0.138035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en el gráfico que la curva corta el eje en 0 y en 4. Luego, estos son los límites de integración.:@0.207764:0.154705:0.926994:0.154705:0.926994:0.138992:0.207764:0.138992:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.472718:0.154705:0.480172:0.154705:0.480172:0.139269:0.472718:0.139269:0.000000 x:@0.505298:0.154705:0.512753:0.154705:0.512753:0.139269:0.505298:0.139269:0.000000 5:@0.516030:0.154150:0.531363:0.154150:0.531363:0.140434:0.516030:0.140434:0.000000 x:@0.579995:0.154705:0.587450:0.154705:0.587450:0.139269:0.579995:0.139269:0.000000 5:@0.590726:0.154150:0.606060:0.154150:0.606060:0.140434:0.590726:0.140434:0.000000 :@0.111037:0.216029:0.115251:0.216029:0.115251:0.199602:0.111037:0.199602:0.000000 Área de la región :@0.134745:0.216029:0.288953:0.216029:0.288953:0.199602:0.134745:0.199602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.268708:0.215449:0.284738:0.215449:0.284738:0.201110:0.268708:0.201110:0.000000 #:@0.288953:0.218356:0.295466:0.218356:0.295466:0.195887:0.288953:0.195887:0.000000 4:@0.297040:0.203721:0.302757:0.203721:0.302757:0.193722:0.297040:0.193722:0.000000 0:@0.297040:0.221372:0.302757:0.221372:0.302757:0.211373:0.297040:0.211373:0.000000 (4 ) .:@0.312492:0.216029:0.398425:0.216029:0.398425:0.199602:0.312492:0.199602:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.326983:0.216029:0.334777:0.216029:0.334777:0.199892:0.326983:0.199892:0.000000 2:@0.338991:0.215449:0.355022:0.215449:0.355022:0.201110:0.338991:0.201110:0.000000 x dx:@0.359236:0.216029:0.395077:0.216029:0.395077:0.199892:0.359236:0.199892:0.000000:0.000000:0.000000:0.000000 2:@0.367030:0.209688:0.372505:0.209688:0.372505:0.200112:0.367030:0.200112:0.000000 16. :@0.073089:0.284185:0.099467:0.284185:0.099467:0.267515:0.073089:0.267515:0.000000:0.000000:0.000000:0.000000 Determinen:@0.103210:0.284185:0.198723:0.284185:0.198723:0.267238:0.103210:0.267238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el área de la región limitada por la parábola 3 3 y las rectas 0, 1 y 1. :@0.198725:0.284185:0.930805:0.284185:0.930805:0.267515:0.198725:0.267515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.542720:0.284185:0.550837:0.284185:0.550837:0.267501:0.542720:0.267501:0.000000 5:@0.555255:0.283630:0.570588:0.283630:0.570588:0.269914:0.555255:0.269914:0.000000 x:@0.575006:0.284185:0.583124:0.284185:0.583124:0.267501:0.575006:0.267501:0.000000 2:@0.583156:0.278121:0.588661:0.278121:0.588661:0.268402:0.583156:0.268402:0.000000 2:@0.593071:0.283630:0.608404:0.283630:0.608404:0.269914:0.593071:0.269914:0.000000 x:@0.622283:0.284185:0.630401:0.284185:0.630401:0.267501:0.622283:0.267501:0.000000 2:@0.634818:0.283630:0.650152:0.283630:0.650152:0.269914:0.634818:0.269914:0.000000 y:@0.756783:0.284185:0.764901:0.284185:0.764901:0.267501:0.756783:0.267501:0.000000 5:@0.769320:0.283630:0.784654:0.283630:0.784654:0.269914:0.769320:0.269914:0.000000 x:@0.806761:0.284185:0.814878:0.284185:0.814878:0.267501:0.806761:0.267501:0.000000 5 2:@0.819296:0.283630:0.854380:0.283630:0.854380:0.269914:0.819296:0.269914:0.000000:0.000000:0.000000 x:@0.881347:0.284185:0.889464:0.284185:0.889464:0.267501:0.881347:0.267501:0.000000 5:@0.893882:0.283630:0.909215:0.283630:0.909215:0.269914:0.893882:0.269914:0.000000 Observen:@0.103199:0.302463:0.179675:0.302463:0.179675:0.285516:0.103199:0.285516:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el gráfico.:@0.179589:0.302463:0.256402:0.302463:0.256402:0.285793:0.179589:0.285793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.504366:0.420902:0.510899:0.420902:0.510899:0.409475:0.504366:0.409475:0.000000 2:@0.431072:0.420499:0.442223:0.420499:0.442223:0.410524:0.431072:0.410524:0.000000 1:@0.442223:0.420902:0.448756:0.420902:0.448756:0.409475:0.442223:0.409475:0.000000 x:@0.636090:0.440322:0.642910:0.440322:0.642910:0.426751:0.636090:0.426751:0.000000 y:@0.457962:0.356745:0.464957:0.356745:0.464957:0.343175:0.457962:0.343175:0.000000 En los ejercicios 17, 18 y 19, encuentra el área bajo la curva dada y el eje x entre los extremos provistos::@0.073089:0.575030:0.846610:0.575030:0.846610:0.558360:0.073089:0.558360:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 17. , 1,3 :@0.073089:0.627261:0.181677:0.627261:0.181677:0.610591:0.073089:0.610591:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.103210:0.627261:0.111327:0.627261:0.111327:0.610578:0.103210:0.610578:0.000000 5:@0.115082:0.626706:0.130416:0.626706:0.130416:0.612991:0.115082:0.612991:0.000000 x:@0.134152:0.627261:0.142270:0.627261:0.142270:0.610578:0.134152:0.610578:0.000000 3:@0.142200:0.621197:0.147705:0.621197:0.147705:0.611479:0.142200:0.611479:0.000000 18. :@0.073089:0.679492:0.115156:0.679492:0.115156:0.662823:0.073089:0.662823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.103210:0.679492:0.111327:0.679492:0.111327:0.662809:0.103210:0.662809:0.000000 5:@0.115082:0.678938:0.130416:0.678938:0.130416:0.665222:0.115082:0.665222:0.000000 cosx:@0.130324:0.679492:0.165598:0.679492:0.165598:0.662809:0.130324:0.662809:0.000000:0.000000:0.000000:0.000000:0.000000 , 0 /2 :@0.165555:0.679492:0.218071:0.679492:0.218071:0.662823:0.165555:0.662823:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.186300:0.678938:0.198578:0.678938:0.198578:0.665222:0.186300:0.665222:0.000000 19. :@0.073089:0.731724:0.115156:0.731724:0.115156:0.715054:0.073089:0.715054:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.103210:0.731724:0.111327:0.731724:0.111327:0.715040:0.103210:0.715040:0.000000 5 :@0.115082:0.731169:0.134926:0.731169:0.134926:0.717453:0.115082:0.717453:0.000000:0.000000 1:@0.134874:0.722499:0.144317:0.722499:0.144317:0.705829:0.134874:0.705829:0.000000 x:@0.135537:0.738891:0.143654:0.738891:0.143654:0.722208:0.135537:0.722208:0.000000 , 1,4:@0.144262:0.731721:0.174376:0.731721:0.174376:0.715052:0.144262:0.715052:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.174358:0.731167:0.178960:0.731167:0.178960:0.717451:0.174358:0.717451:0.000000 En los ejercicios 20, 21 y 22, encuentra el área entre las curvas dadas y entre los extremos provistos::@0.073081:0.783949:0.822530:0.783949:0.822530:0.767279:0.073081:0.767279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 20. , 4:@0.073089:0.836188:0.199417:0.836188:0.199417:0.819518:0.073089:0.819518:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.107034:0.836188:0.115152:0.836188:0.115152:0.819504:0.107034:0.819504:0.000000 5:@0.118907:0.835633:0.134240:0.835633:0.134240:0.821917:0.118907:0.821917:0.000000 x y:@0.137977:0.836188:0.167149:0.836188:0.167149:0.819504:0.137977:0.819504:0.000000:0.000000:0.000000 2:@0.146024:0.830124:0.151529:0.830124:0.151529:0.820406:0.146024:0.820406:0.000000 5:@0.170904:0.835633:0.186237:0.835633:0.186237:0.821917:0.170904:0.821917:0.000000 x x:@0.199325:0.836188:0.237299:0.836188:0.237299:0.819504:0.199325:0.819504:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.210663:0.835633:0.225997:0.835633:0.225997:0.821917:0.210663:0.821917:0.000000 2:@0.237252:0.830124:0.242757:0.830124:0.242757:0.820406:0.237252:0.820406:0.000000 , 0,2:@0.242712:0.836188:0.272826:0.836188:0.272826:0.819518:0.242712:0.819518:0.000000:0.000000:0.000000:0.000000:0.000000 21. :@0.073089:0.888419:0.134226:0.888419:0.134226:0.871750:0.073089:0.871750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.103210:0.888419:0.111327:0.888419:0.111327:0.871736:0.103210:0.871736:0.000000 5:@0.115082:0.887865:0.130416:0.887865:0.130416:0.874149:0.115082:0.874149:0.000000 x, y:@0.147906:0.888419:0.171155:0.888419:0.171155:0.871736:0.147906:0.871736:0.000000:0.000000:0.000000:0.000000 , 0,1 :@0.177356:0.888419:0.242316:0.888419:0.242316:0.871750:0.177356:0.871750:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.181185:0.887865:0.196518:0.887865:0.196518:0.874149:0.181185:0.874149:0.000000 x:@0.200255:0.888419:0.208373:0.888419:0.208373:0.871736:0.200255:0.871736:0.000000 22. :@0.073089:0.940651:0.134226:0.940651:0.134226:0.923981:0.073089:0.923981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y:@0.103210:0.940651:0.111327:0.940651:0.111327:0.923967:0.103210:0.923967:0.000000 5:@0.115082:0.940096:0.130416:0.940096:0.130416:0.926380:0.115082:0.926380:0.000000 senx y:@0.134152:0.940651:0.182637:0.940651:0.182637:0.923967:0.134152:0.923967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.166973:0.940651:0.205536:0.940651:0.205536:0.923981:0.166973:0.923981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.186392:0.940096:0.201725:0.940096:0.201725:0.926380:0.186392:0.926380:0.000000 cosx, :@0.205462:0.940651:0.244548:0.940651:0.244548:0.923967:0.205462:0.923967:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 0, /4 :@0.244504:0.940651:0.293191:0.940651:0.293191:0.923981:0.244504:0.923981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.261420:0.940096:0.273698:0.940096:0.273698:0.926380:0.261420:0.926380:0.000000 2 :@0.455411:0.717891:0.463693:0.717891:0.463693:0.707892:0.455411:0.707892:0.000000:0.000000 In u:@0.463693:0.717891:0.484361:0.717891:0.484361:0.708068:0.463693:0.708068:0.000000:0.000000:0.000000:0.000000 2:@0.472174:0.714032:0.475506:0.714032:0.475506:0.708203:0.472174:0.708203:0.000000 :@0.475505:0.717538:0.478434:0.717538:0.478434:0.708810:0.475505:0.708810:0.000000 2:@0.484361:0.714032:0.487693:0.714032:0.487693:0.708203:0.484361:0.708203:0.000000 20 :@0.452448:0.621399:0.466446:0.621399:0.466446:0.611400:0.452448:0.611400:0.000000:0.000000:0.000000 u:@0.466446:0.621399:0.472373:0.621399:0.472373:0.611576:0.466446:0.611576:0.000000 2:@0.472371:0.617540:0.475704:0.617540:0.475704:0.611710:0.472371:0.611710:0.000000 2 :@0.686774:0.532950:0.699460:0.532950:0.699460:0.524222:0.686774:0.524222:0.000000:0.000000 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