187:@0.916858:0.966074:0.945034:0.966074:0.945034:0.949450:0.916858:0.949450:0.000000:0.000000:0.000000
donde::@0.131968:0.096194:0.181614:0.096194:0.181614:0.079697:0.131968:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.108233:0.120674:0.112375:0.120674:0.112375:0.104176:0.108233:0.104176:0.000000
3       = (  + 1)  –      (  + 1) –   =  (  + 1),:@0.210801:0.120674:0.516946:0.120674:0.516946:0.104176:0.210801:0.104176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.240007:0.120790:0.243860:0.120790:0.243860:0.104321:0.240007:0.104321:0.000000
2:@0.243859:0.114321:0.248812:0.114321:0.248812:0.104703:0.243859:0.104703:0.000000
n:@0.273857:0.120790:0.283220:0.120790:0.283220:0.104321:0.273857:0.104321:0.000000
3:@0.316760:0.114321:0.321713:0.114321:0.321713:0.104703:0.316760:0.104703:0.000000
n n:@0.356293:0.120790:0.380202:0.120790:0.380202:0.104321:0.356293:0.104321:0.000000:0.000000:0.000000
n n n:@0.430599:0.120790:0.481421:0.120790:0.481421:0.104321:0.430599:0.104321:0.000000:0.000000:0.000000:0.000000:0.000000
S:@0.250952:0.162619:0.258831:0.162619:0.258831:0.146150:0.250952:0.146150:0.000000
n:@0.258755:0.165848:0.264214:0.165848:0.264214:0.156247:0.258755:0.156247:0.000000
 =       = 0  + 1  + 2  + … +  ;:@0.264213:0.162503:0.476792:0.162503:0.476792:0.146005:0.264213:0.146005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.299873:0.162619:0.303726:0.162619:0.303726:0.146150:0.299873:0.146150:0.000000
2:@0.303918:0.156150:0.308871:0.156150:0.308871:0.146532:0.303918:0.146532:0.000000
2:@0.336458:0.156150:0.341411:0.156150:0.341411:0.146532:0.336458:0.146532:0.000000
2:@0.368999:0.156150:0.373952:0.156150:0.373952:0.146532:0.368999:0.146532:0.000000
2:@0.401539:0.156150:0.406492:0.156150:0.406492:0.146532:0.401539:0.146532:0.000000
n:@0.459723:0.162619:0.469086:0.162619:0.469086:0.146150:0.459723:0.146150:0.000000
2:@0.469085:0.156150:0.474038:0.156150:0.474038:0.146532:0.469085:0.146532:0.000000
 :@0.108229:0.200761:0.112371:0.200761:0.112371:0.184264:0.108229:0.184264:0.000000
           =                                .:@0.267649:0.200761:0.460090:0.200761:0.460090:0.184264:0.267649:0.184264:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Definición :@0.108229:0.243054:0.195096:0.243054:0.195096:0.226108:0.108229:0.226108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
. Sea [ ,  ] un intervalo cerrado de,  ,      . Una parti-:@0.188315:0.242591:0.595761:0.242598:0.595761:0.226100:0.188315:0.226094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.230274:0.242707:0.255955:0.242707:0.255955:0.226238:0.230274:0.226238:0.000000:0.000000:0.000000
:@0.442319:0.241511:0.455624:0.241511:0.455624:0.228649:0.442319:0.228649:0.000000
n:@0.463059:0.242714:0.472422:0.242714:0.472422:0.226245:0.463059:0.226245:0.000000
:@0.477111:0.242079:0.491763:0.242079:0.491763:0.228706:0.477111:0.228706:0.000000
Z:@0.496448:0.241511:0.508739:0.241511:0.508739:0.228649:0.496448:0.228649:0.000000
+:@0.508739:0.234988:0.515040:0.234988:0.515040:0.225370:0.508739:0.225370:0.000000
ción del intervalo [ ,  ] en   subintervalos es un conjunto de puntos :@0.108235:0.259949:0.599930:0.259949:0.599930:0.243451:0.108235:0.243451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.241993:0.260065:0.267250:0.260065:0.267250:0.243596:0.241993:0.243596:0.000000:0.000000:0.000000
n:@0.299201:0.260065:0.308564:0.260065:0.308564:0.243596:0.299201:0.243596:0.000000
que se nota  ( ) y se define como: :@0.108235:0.277300:0.357886:0.277300:0.357886:0.260802:0.108235:0.260802:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.195145:0.276385:0.202955:0.276385:0.205091:0.263328:0.197281:0.263328:0.000000
n:@0.210241:0.277415:0.219604:0.277415:0.219604:0.260947:0.210241:0.260947:0.000000
:@0.267690:0.304297:0.275500:0.304297:0.277635:0.291241:0.269825:0.291241:0.000000
( ) = { ,  , …, :@0.276833:0.305212:0.383642:0.305212:0.383642:0.288714:0.276833:0.288714:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.282785:0.305327:0.292148:0.305327:0.292148:0.288859:0.282785:0.288859:0.000000
x x:@0.323050:0.305327:0.349848:0.305327:0.349848:0.288859:0.323050:0.288859:0.000000:0.000000:0.000000
0:@0.330524:0.308490:0.335477:0.308490:0.335477:0.298872:0.330524:0.298872:0.000000
1:@0.349848:0.308490:0.354801:0.308490:0.354801:0.298872:0.349848:0.298872:0.000000
x:@0.383642:0.305327:0.391117:0.305327:0.391117:0.288859:0.383642:0.288859:0.000000
n:@0.390998:0.308557:0.396457:0.308557:0.396457:0.298956:0.390998:0.298956:0.000000
–1:@0.396457:0.308490:0.407531:0.308490:0.407531:0.298872:0.396457:0.298872:0.000000:0.000000
,  },:@0.407531:0.305212:0.435857:0.305212:0.435857:0.288714:0.407531:0.288714:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.414428:0.305327:0.421903:0.305327:0.421903:0.288859:0.414428:0.288859:0.000000
n:@0.421788:0.308557:0.427246:0.308557:0.427246:0.298956:0.421788:0.298956:0.000000
donde::@0.108232:0.329691:0.157879:0.329691:0.157879:0.313193:0.108232:0.313193:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.253396:0.347157:0.260871:0.347157:0.260871:0.330688:0.253396:0.330688:0.000000
0:@0.260871:0.350319:0.265824:0.350319:0.265824:0.340701:0.260871:0.340701:0.000000
 =   <   < … :@0.265823:0.347041:0.363691:0.347041:0.363691:0.330543:0.265823:0.330543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a x:@0.284915:0.347157:0.320459:0.347157:0.320459:0.330688:0.284915:0.330688:0.000000:0.000000:0.000000
1:@0.320459:0.350319:0.325412:0.350319:0.325412:0.340701:0.320459:0.340701:0.000000
x:@0.363691:0.347157:0.371166:0.347157:0.371166:0.330688:0.363691:0.330688:0.000000
n:@0.371050:0.350386:0.376508:0.350386:0.376508:0.340785:0.371050:0.340785:0.000000
–1:@0.376508:0.350319:0.387583:0.350319:0.387583:0.340701:0.376508:0.340701:0.000000:0.000000
 <   =  .:@0.387583:0.347041:0.450606:0.347041:0.450606:0.330543:0.387583:0.330543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.406674:0.347157:0.414149:0.347157:0.414149:0.330688:0.406674:0.330688:0.000000
n:@0.414033:0.350386:0.419492:0.350386:0.419492:0.340785:0.414033:0.340785:0.000000
b:@0.438584:0.347157:0.447851:0.347157:0.447851:0.330688:0.438584:0.330688:0.000000
 :@0.108243:0.364392:0.112385:0.364392:0.112385:0.347894:0.108243:0.347894:0.000000
Al conjunto  ( ) se le llama subdivisión del intervalo [ ,  ]. Escribire-:@0.108243:0.381742:0.595762:0.381742:0.595762:0.365245:0.108243:0.365245:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.197403:0.380828:0.205213:0.380828:0.207349:0.367771:0.199539:0.367771:0.000000
n:@0.212499:0.381858:0.221862:0.381858:0.221862:0.365389:0.212499:0.365389:0.000000
a b:@0.492421:0.381858:0.517738:0.381858:0.517738:0.365389:0.492421:0.365389:0.000000:0.000000:0.000000
mos también::@0.108236:0.399093:0.205872:0.399093:0.205872:0.382595:0.108236:0.382595:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.195177:0.422658:0.202987:0.422658:0.205123:0.409602:0.197313:0.409602:0.000000
( ) = {    [ ,  ] |   =   <   < … <   =  }.:@0.204320:0.423573:0.508372:0.423573:0.508372:0.407075:0.204320:0.407075:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.210273:0.423688:0.219636:0.423688:0.219636:0.407220:0.210273:0.407220:0.000000
x:@0.250537:0.423688:0.258012:0.423688:0.258012:0.407220:0.250537:0.407220:0.000000
j:@0.258011:0.426917:0.260258:0.426917:0.260258:0.417316:0.258011:0.417316:0.000000
:@0.264399:0.423054:0.279051:0.423054:0.279051:0.409681:0.264399:0.409681:0.000000
a b x:@0.289049:0.423688:0.340815:0.423688:0.340815:0.407220:0.289049:0.407220:0.000000:0.000000:0.000000:0.000000:0.000000
0:@0.340813:0.426849:0.345766:0.426849:0.345766:0.417231:0.340813:0.417231:0.000000
a x:@0.364859:0.423688:0.400403:0.423688:0.400403:0.407220:0.364859:0.407220:0.000000:0.000000:0.000000
1:@0.400402:0.426849:0.405355:0.426849:0.405355:0.417231:0.400402:0.417231:0.000000
x:@0.458585:0.423688:0.466060:0.423688:0.466060:0.407220:0.458585:0.407220:0.000000
n:@0.465942:0.426917:0.471401:0.426917:0.471401:0.417316:0.465942:0.417316:0.000000
b:@0.490493:0.423688:0.499760:0.423688:0.499760:0.407220:0.490493:0.407220:0.000000
 :@0.108232:0.440924:0.112374:0.440924:0.112374:0.424426:0.108232:0.424426:0.000000
En la Figura 6.3. se muestra una partición  ( ) del intervalo [ ,  ].:@0.108232:0.458274:0.566799:0.458274:0.566799:0.441777:0.108232:0.441777:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.400164:0.457360:0.407974:0.457360:0.410110:0.444303:0.402300:0.444303:0.000000
n:@0.415260:0.458390:0.424623:0.458390:0.424623:0.441921:0.415260:0.441921:0.000000
a b:@0.533046:0.458390:0.558187:0.458390:0.558187:0.441921:0.533046:0.441921:0.000000:0.000000:0.000000
Los   subintervalos son:  [ ,  ], [ ,  ], …, [:@0.108230:0.571430:0.413282:0.571431:0.413282:0.554934:0.108230:0.554932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.136107:0.571546:0.145469:0.571546:0.145469:0.555077:0.136107:0.555077:0.000000
x x:@0.290612:0.571546:0.317414:0.571547:0.317414:0.555078:0.290612:0.555077:0.000000:0.000000:0.000000
0:@0.298088:0.574708:0.303041:0.574708:0.303041:0.565090:0.298088:0.565090:0.000000
1:@0.317414:0.574708:0.322367:0.574708:0.322367:0.565090:0.317414:0.565090:0.000000
x x:@0.340976:0.571547:0.367775:0.571547:0.367775:0.555078:0.340976:0.555078:0.000000:0.000000:0.000000
1:@0.348451:0.574708:0.353404:0.574708:0.353404:0.565090:0.348451:0.565090:0.000000
2:@0.367775:0.574708:0.372728:0.574708:0.372728:0.565090:0.367775:0.565090:0.000000
x:@0.413282:0.571547:0.420757:0.571547:0.420757:0.555078:0.413282:0.555078:0.000000
n:@0.420638:0.574776:0.426097:0.574776:0.426097:0.565174:0.420638:0.565174:0.000000
–1:@0.426097:0.574708:0.437171:0.574708:0.437171:0.565090:0.426097:0.565090:0.000000:0.000000
,  ],:@0.437171:0.571431:0.465497:0.571431:0.465497:0.554934:0.437171:0.554934:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.444068:0.571547:0.451543:0.571547:0.451543:0.555078:0.444068:0.555078:0.000000
n:@0.451428:0.574776:0.456886:0.574776:0.456886:0.565174:0.451428:0.565174:0.000000
 :@0.108242:0.588782:0.112384:0.588782:0.112384:0.572284:0.108242:0.572284:0.000000
que abreviadamente escribimos [:@0.108242:0.606133:0.345511:0.606133:0.345511:0.589635:0.108242:0.589635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.345511:0.606249:0.352986:0.606249:0.352986:0.589780:0.345511:0.589780:0.000000
j:@0.352969:0.609477:0.355215:0.609477:0.355215:0.599876:0.352969:0.599876:0.000000
–1:@0.355215:0.609410:0.366289:0.609410:0.366289:0.599791:0.355215:0.599791:0.000000:0.000000
,  ],   = 1, …,  , lo cual se lee “in-:@0.366290:0.606133:0.595833:0.606133:0.595833:0.589635:0.366290:0.589635:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x j:@0.373669:0.606249:0.400468:0.606249:0.400468:0.589780:0.373669:0.589780:0.000000:0.000000:0.000000
j:@0.381135:0.609477:0.383381:0.609477:0.383381:0.599876:0.381135:0.599876:0.000000
n:@0.458813:0.606249:0.468176:0.606249:0.468176:0.589780:0.458813:0.589780:0.000000
tervalo cerrado [:@0.108233:0.623484:0.228254:0.623484:0.228254:0.606986:0.108233:0.606986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.228275:0.623599:0.235750:0.623599:0.235750:0.607131:0.228275:0.607131:0.000000
j:@0.235741:0.626828:0.237987:0.626828:0.237987:0.617227:0.235741:0.617227:0.000000
–1:@0.237987:0.626760:0.249061:0.626760:0.249061:0.617142:0.237987:0.617142:0.000000:0.000000
,  ] con   que varía de 1 a  ”. El intervalo [:@0.249060:0.623484:0.551406:0.623484:0.551406:0.606986:0.249060:0.606986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.256978:0.623599:0.264453:0.623599:0.264453:0.607131:0.256978:0.607131:0.000000
j:@0.264459:0.626828:0.266706:0.626828:0.266706:0.617227:0.264459:0.617227:0.000000
j:@0.309841:0.623599:0.313694:0.623599:0.313694:0.607131:0.309841:0.607131:0.000000
n:@0.438993:0.623599:0.448356:0.623599:0.448356:0.607131:0.438993:0.607131:0.000000
x:@0.551406:0.623599:0.558881:0.623599:0.558881:0.607131:0.551406:0.607131:0.000000
j:@0.558946:0.626828:0.561193:0.626828:0.561193:0.617227:0.558946:0.617227:0.000000
–1:@0.561193:0.626760:0.572267:0.626760:0.572267:0.617142:0.561193:0.617142:0.000000:0.000000
,  ] :@0.572266:0.623484:0.599910:0.623484:0.599910:0.606986:0.572266:0.606986:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.580184:0.623599:0.587659:0.623599:0.587659:0.607131:0.580184:0.607131:0.000000
j:@0.587665:0.626828:0.589911:0.626828:0.589911:0.617227:0.587665:0.617227:0.000000
se llama j-ésimo intervalo de [ ,  ]. Las longitudes de cada uno de los :@0.108241:0.640834:0.599906:0.640834:0.599906:0.624337:0.108241:0.624337:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.319192:0.640950:0.344202:0.640950:0.344202:0.624481:0.319192:0.624481:0.000000:0.000000:0.000000
intervalos son::@0.108241:0.658185:0.209806:0.658185:0.209806:0.641687:0.108241:0.641687:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.207419:0.682780:0.216820:0.682780:0.216820:0.666311:0.207419:0.666311:0.000000
1:@0.216812:0.685940:0.221765:0.685940:0.221765:0.676322:0.216812:0.676322:0.000000
 =   –  ,    =   –  , …,   =   – :@0.221764:0.682664:0.469270:0.682664:0.469270:0.666166:0.221764:0.666166:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.240856:0.682779:0.248331:0.682779:0.248331:0.666310:0.240856:0.666310:0.000000
1:@0.248330:0.685940:0.253283:0.685940:0.253283:0.676322:0.248330:0.676322:0.000000
x h:@0.272067:0.682779:0.304936:0.682779:0.304936:0.666310:0.272067:0.666310:0.000000:0.000000:0.000000
0:@0.279541:0.685940:0.284495:0.685940:0.284495:0.676322:0.279541:0.676322:0.000000
2:@0.304935:0.685940:0.309888:0.685940:0.309888:0.676322:0.304935:0.676322:0.000000
x:@0.328980:0.682779:0.336455:0.682779:0.336455:0.666310:0.328980:0.666310:0.000000
2:@0.336454:0.685940:0.341407:0.685940:0.341407:0.676322:0.336454:0.676322:0.000000
x:@0.360190:0.682779:0.367665:0.682779:0.367665:0.666310:0.360190:0.666310:0.000000
1:@0.367666:0.685940:0.372619:0.685940:0.372619:0.676322:0.367666:0.676322:0.000000
h:@0.405600:0.682779:0.415001:0.682779:0.415001:0.666310:0.405600:0.666310:0.000000
n:@0.414847:0.686008:0.420306:0.686008:0.420306:0.676406:0.414847:0.676406:0.000000
 :@0.420306:0.685940:0.422721:0.685940:0.422721:0.676322:0.420306:0.676322:0.000000
x:@0.437669:0.682779:0.445144:0.682779:0.445144:0.666310:0.437669:0.666310:0.000000
n:@0.445028:0.686008:0.450487:0.686008:0.450487:0.676406:0.445028:0.676406:0.000000
x:@0.469270:0.682779:0.476745:0.682779:0.476745:0.666310:0.469270:0.666310:0.000000
n:@0.476630:0.686008:0.482089:0.686008:0.482089:0.676406:0.476630:0.676406:0.000000
–1:@0.482089:0.685940:0.493163:0.685940:0.493163:0.676322:0.482089:0.676322:0.000000:0.000000
,:@0.493836:0.682664:0.496591:0.682664:0.496591:0.666166:0.493836:0.666166:0.000000
 :@0.108242:0.700014:0.112384:0.700014:0.112384:0.683517:0.108242:0.683517:0.000000
que abreviadamente escribimos  =   – :@0.108242:0.717365:0.395658:0.717365:0.395658:0.700867:0.108242:0.700867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.338227:0.717481:0.347628:0.717481:0.347628:0.701012:0.338227:0.701012:0.000000
j:@0.347543:0.720709:0.349789:0.720709:0.349789:0.711108:0.347543:0.711108:0.000000
 :@0.349789:0.720642:0.352204:0.720642:0.352204:0.711024:0.349789:0.711024:0.000000
x:@0.367153:0.717481:0.374628:0.717481:0.374628:0.701012:0.367153:0.701012:0.000000
j:@0.374628:0.720709:0.376874:0.720709:0.376874:0.711108:0.374628:0.711108:0.000000
x:@0.395658:0.717481:0.403133:0.717481:0.403133:0.701012:0.395658:0.701012:0.000000
j:@0.403132:0.720709:0.405379:0.720709:0.405379:0.711108:0.403132:0.711108:0.000000
–1:@0.405379:0.720642:0.416453:0.720642:0.416453:0.711024:0.405379:0.711024:0.000000:0.000000
,    = 1, …,  , que se lee :@0.417127:0.717365:0.578915:0.717365:0.578915:0.700867:0.417127:0.700867:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.428166:0.717481:0.432019:0.717481:0.432019:0.701012:0.428166:0.701012:0.000000
n:@0.488447:0.717481:0.497810:0.717481:0.497810:0.701012:0.488447:0.701012:0.000000
“ =   – :@0.108228:0.734716:0.171337:0.734716:0.171337:0.718218:0.108228:0.718218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
h:@0.113892:0.734831:0.123293:0.734831:0.123293:0.718363:0.113892:0.718363:0.000000
j:@0.123221:0.738060:0.125468:0.738060:0.125468:0.728459:0.123221:0.728459:0.000000
 :@0.125468:0.737992:0.127883:0.737992:0.127883:0.728374:0.125468:0.728374:0.000000
x:@0.142832:0.734831:0.150307:0.734831:0.150307:0.718363:0.142832:0.718363:0.000000
j:@0.150307:0.738060:0.152553:0.738060:0.152553:0.728459:0.150307:0.728459:0.000000
x:@0.171337:0.734831:0.178812:0.734831:0.178812:0.718363:0.171337:0.718363:0.000000
j:@0.178811:0.738060:0.181057:0.738060:0.181057:0.728459:0.178811:0.728459:0.000000
–1:@0.181057:0.737992:0.192132:0.737992:0.192132:0.728374:0.181057:0.728374:0.000000:0.000000
 con   que varía de 1 a  ”. Se tiene::@0.192806:0.734716:0.430285:0.734716:0.430285:0.718218:0.192806:0.718218:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
j:@0.228042:0.734831:0.231895:0.734831:0.231895:0.718363:0.228042:0.718363:0.000000
n:@0.351068:0.734831:0.360431:0.734831:0.360431:0.718363:0.351068:0.718363:0.000000
[ ,  ] = [ ,  ]   [ ,  ]   … :@0.108231:0.769417:0.321375:0.769417:0.321375:0.752920:0.108231:0.752920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.114088:0.769533:0.139229:0.769533:0.139229:0.753064:0.114088:0.753064:0.000000:0.000000:0.000000
x x:@0.170034:0.769533:0.196833:0.769533:0.196833:0.753064:0.170034:0.753064:0.000000:0.000000:0.000000
0:@0.177509:0.772694:0.182462:0.772694:0.182462:0.763076:0.177509:0.763076:0.000000
1:@0.196833:0.772694:0.201786:0.772694:0.201786:0.763076:0.196833:0.763076:0.000000
:@0.211785:0.769200:0.227833:0.769200:0.227833:0.754553:0.211785:0.754553:0.000000
x x:@0.237832:0.769533:0.264630:0.769533:0.264630:0.753064:0.237832:0.753064:0.000000:0.000000:0.000000
1:@0.245306:0.772694:0.250259:0.772694:0.250259:0.763076:0.245306:0.763076:0.000000
2 :@0.264630:0.772694:0.271998:0.772694:0.271998:0.763076:0.264630:0.763076:0.000000:0.000000
:@0.281996:0.769200:0.298044:0.769200:0.298044:0.754553:0.281996:0.754553:0.000000
 :@0.321375:0.769200:0.342239:0.769200:0.342239:0.754553:0.321375:0.754553:0.000000:0.000000
[:@0.342239:0.769417:0.348096:0.769417:0.348096:0.752920:0.342239:0.752920:0.000000
x:@0.348096:0.769533:0.355570:0.769533:0.355570:0.753064:0.348096:0.753064:0.000000
n–:@0.355453:0.772761:0.366763:0.772761:0.366763:0.763160:0.355453:0.763160:0.000000:0.000000
1:@0.366763:0.772694:0.371717:0.772694:0.371717:0.763076:0.366763:0.763076:0.000000
,  ] = [:@0.371716:0.769417:0.422236:0.769417:0.422236:0.752920:0.371716:0.752920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.378613:0.769533:0.386088:0.769533:0.386088:0.753064:0.378613:0.753064:0.000000
n:@0.385973:0.772761:0.391431:0.772761:0.391431:0.763160:0.385973:0.763160:0.000000
x:@0.422236:0.769533:0.429711:0.769533:0.429711:0.753064:0.422236:0.753064:0.000000
j:@0.429710:0.772761:0.431956:0.772761:0.431956:0.763160:0.429710:0.763160:0.000000
–1:@0.431956:0.772694:0.443031:0.772694:0.443031:0.763076:0.431956:0.763076:0.000000:0.000000
 –  ] =       [:@0.443030:0.769417:0.525841:0.769417:0.525841:0.752920:0.443030:0.752920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.461813:0.769533:0.469288:0.769533:0.469288:0.753064:0.461813:0.753064:0.000000
j:@0.469287:0.772761:0.471534:0.772761:0.471534:0.763160:0.469287:0.763160:0.000000
x:@0.525841:0.769533:0.533316:0.769533:0.533316:0.753064:0.525841:0.753064:0.000000
j:@0.533317:0.772761:0.535563:0.772761:0.535563:0.763160:0.533317:0.763160:0.000000
–1:@0.535563:0.772694:0.546637:0.772694:0.546637:0.763076:0.535563:0.763076:0.000000:0.000000
 –  ].:@0.546637:0.769417:0.583752:0.769417:0.583752:0.752920:0.546637:0.752920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.565420:0.769533:0.572895:0.769533:0.572895:0.753064:0.565420:0.753064:0.000000
j:@0.572894:0.772761:0.575141:0.772761:0.575141:0.763160:0.572894:0.763160:0.000000
 :@0.108228:0.786768:0.112370:0.786768:0.112370:0.770270:0.108228:0.770270:0.000000
Notemos que los extremos del intervalo [ ,  ] pertenecen a  ( ), esto :@0.108228:0.804119:0.599906:0.804119:0.599906:0.787621:0.108228:0.787621:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.399654:0.804234:0.424313:0.804234:0.424313:0.787766:0.399654:0.787766:0.000000:0.000000:0.000000
:@0.529268:0.803204:0.537078:0.803204:0.539214:0.790148:0.531404:0.790148:0.000000
n:@0.544364:0.804234:0.553727:0.804234:0.553727:0.787766:0.544364:0.787766:0.000000
es,  ,      ( ). Además,  ( ) tiene exactamente   + 1 puntos distin-:@0.108237:0.821470:0.595724:0.821470:0.595724:0.804972:0.108237:0.804972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.130103:0.821585:0.155591:0.821585:0.155591:0.805116:0.130103:0.805116:0.000000:0.000000:0.000000
:@0.160093:0.820951:0.174746:0.820951:0.174746:0.807578:0.160093:0.807578:0.000000
:@0.178786:0.820555:0.186596:0.820555:0.188732:0.807498:0.180922:0.807498:0.000000
n:@0.193882:0.821585:0.203245:0.821585:0.203245:0.805116:0.193882:0.805116:0.000000
:@0.282078:0.820555:0.289888:0.820555:0.292024:0.807498:0.284214:0.807498:0.000000
n:@0.297174:0.821585:0.306537:0.821585:0.306537:0.805116:0.297174:0.805116:0.000000
n:@0.454165:0.821585:0.463528:0.821585:0.463528:0.805116:0.454165:0.805116:0.000000
tos del intervalo [ ,  ].:@0.108240:0.838820:0.266252:0.838820:0.266252:0.822323:0.108240:0.822323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.232499:0.838936:0.257640:0.838936:0.257640:0.822467:0.232499:0.822467:0.000000:0.000000:0.000000
Se llama partición uniforme  ( ) a la partición de [ ,  ] dada por:  :@0.108240:0.873522:0.578667:0.873522:0.578667:0.857024:0.108240:0.857024:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.308830:0.872607:0.316640:0.872607:0.318776:0.859551:0.310966:0.859551:0.000000
n:@0.323926:0.873637:0.333289:0.873637:0.333289:0.857169:0.323926:0.857169:0.000000
a b:@0.467393:0.873637:0.492534:0.873637:0.492534:0.857169:0.467393:0.857169:0.000000:0.000000:0.000000
x:@0.199511:0.901673:0.206986:0.901673:0.206986:0.885205:0.199511:0.885205:0.000000
j:@0.206988:0.904909:0.209235:0.904909:0.209235:0.895308:0.206988:0.895308:0.000000
 =   +  ,     = 0, 1, …,  , donde   =            .:@0.209235:0.901565:0.504492:0.901565:0.504492:0.885067:0.209235:0.885067:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a jh j:@0.228327:0.901680:0.288569:0.901680:0.288569:0.885212:0.228327:0.885212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.360390:0.901680:0.369753:0.901680:0.369753:0.885212:0.360390:0.885212:0.000000
h:@0.427682:0.901680:0.437083:0.901680:0.437083:0.885212:0.427682:0.885212:0.000000
Esta es la partición que utilizamos más adelante.:@0.108227:0.936266:0.448677:0.936266:0.448677:0.919768:0.108227:0.919768:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Recuerda que…:@0.684804:0.106800:0.794564:0.106800:0.794564:0.091327:0.684804:0.091327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
La integral definida cum-:@0.685042:0.135427:0.846641:0.135427:0.846641:0.120364:0.685042:0.120364:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ple las siguientes :@0.638498:0.151269:0.749490:0.151269:0.749490:0.136206:0.638498:0.136206:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
propiedades:@0.749490:0.151691:0.836715:0.151691:0.836715:0.136219:0.749490:0.136219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
::@0.836720:0.151269:0.839236:0.151269:0.839236:0.136206:0.836720:0.136206:0.000000
•:@0.638498:0.174887:0.645587:0.174887:0.645587:0.159190:0.638498:0.159190:0.000000
  Toda integral extendida a un :@0.645586:0.174240:0.844440:0.174240:0.844440:0.159177:0.645586:0.159177:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
intervalo de un solo punto, :@0.655120:0.190082:0.834890:0.190082:0.834890:0.175019:0.655120:0.175019:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
[ ,  ], es igual a cero.:@0.655120:0.205924:0.786940:0.205924:0.786940:0.190861:0.655120:0.190861:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a a:@0.660467:0.206030:0.683159:0.206030:0.683159:0.190993:0.660467:0.190993:0.000000:0.000000:0.000000
•:@0.638498:0.222413:0.645586:0.222413:0.645586:0.206716:0.638498:0.206716:0.000000
  Cuando la función  ( ) es :@0.645586:0.221766:0.821678:0.221766:0.821678:0.206703:0.645586:0.206703:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.779374:0.221872:0.795557:0.221872:0.795557:0.206835:0.779374:0.206835:0.000000:0.000000:0.000000
mayor que cero, su integral :@0.655120:0.237608:0.833395:0.237608:0.833395:0.222545:0.655120:0.222545:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es positiva; si la función es :@0.655120:0.253450:0.827077:0.253450:0.827077:0.238387:0.655120:0.238387:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
menor que cero, su integral :@0.655120:0.269292:0.835486:0.269292:0.835486:0.254229:0.655120:0.254229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
es negativa.:@0.655120:0.285134:0.729366:0.285134:0.729366:0.270071:0.655120:0.270071:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.638498:0.301623:0.645586:0.301623:0.645586:0.285926:0.638498:0.285926:0.000000
  Al permutar los límites de una :@0.645410:0.300976:0.850243:0.300976:0.850243:0.285913:0.645410:0.285913:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
integral, esta cambia de signo.:@0.655120:0.316818:0.842079:0.316818:0.842079:0.301755:0.655120:0.301755:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.638498:0.333307:0.645586:0.333307:0.645586:0.317610:0.638498:0.317610:0.000000
  Dados tres puntos tales que :@0.645586:0.332660:0.839865:0.332660:0.839865:0.317597:0.645586:0.317597:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b c:@0.655120:0.348607:0.713202:0.348607:0.713202:0.333571:0.655120:0.333571:0.000000:0.000000:0.000000:0.000000:0.000000
 <   <  , entonces se cum-:@0.663317:0.348502:0.833921:0.348502:0.833921:0.333439:0.663317:0.333439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ple la integración a trozos::@0.655120:0.364344:0.823789:0.364344:0.823789:0.349281:0.655120:0.349281:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
      ( ):@0.638498:0.387315:0.689245:0.387315:0.689245:0.372252:0.638498:0.372252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x dx :@0.667627:0.387420:0.708084:0.387420:0.708084:0.372384:0.667627:0.372384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+      ( )  =     ( ):@0.708084:0.387315:0.823931:0.387315:0.823931:0.372252:0.708084:0.372252:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x dx:@0.736861:0.387420:0.773536:0.387420:0.773536:0.372384:0.736861:0.372384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x dx.:@0.802313:0.387420:0.841697:0.387420:0.841697:0.372384:0.802313:0.372384:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
•:@0.638498:0.419646:0.645586:0.419646:0.645586:0.403949:0.638498:0.403949:0.000000
  Para todo punto   del inter-:@0.645499:0.418999:0.832656:0.418999:0.832656:0.403936:0.645499:0.403936:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.765251:0.419104:0.772076:0.419104:0.772076:0.404068:0.765251:0.404068:0.000000
valo [ ,  ] al que se aplican :@0.655120:0.434841:0.830598:0.434841:0.830598:0.419778:0.655120:0.419778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a b:@0.690511:0.434946:0.713202:0.434946:0.713202:0.419910:0.690511:0.419910:0.000000:0.000000:0.000000
dos funciones  ( ) y  ( ), tales :@0.655120:0.450683:0.847203:0.450683:0.847203:0.435620:0.655120:0.435620:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.748170:0.450788:0.764178:0.450788:0.764178:0.435752:0.748170:0.435752:0.000000:0.000000:0.000000
g x:@0.783879:0.450788:0.802753:0.450788:0.802753:0.435752:0.783879:0.435752:0.000000:0.000000:0.000000
que  ( ) ≤  ( ), se verifica que::@0.655120:0.466525:0.844828:0.466525:0.844828:0.451462:0.655120:0.451462:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x:@0.683211:0.466630:0.699218:0.466630:0.699218:0.451594:0.683211:0.451594:0.000000:0.000000:0.000000
g x:@0.721646:0.466630:0.740520:0.466630:0.740520:0.451594:0.721646:0.451594:0.000000:0.000000:0.000000
      ( ):@0.638498:0.489496:0.689245:0.489496:0.689245:0.474432:0.638498:0.474432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
f x dx :@0.667627:0.489601:0.708084:0.489601:0.708084:0.474564:0.667627:0.474564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≤      ( ) .:@0.708084:0.489496:0.778919:0.489496:0.778919:0.474432:0.708084:0.474432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
g x dx:@0.736861:0.489601:0.776403:0.489601:0.776403:0.474564:0.736861:0.474564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Adaptado de: :@0.766272:0.644509:0.850078:0.644509:0.850078:0.630881:0.766272:0.630881:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
http://www.hiru.eus/matematicas/:@0.643569:0.658843:0.846656:0.658843:0.846656:0.645214:0.643569:0.645214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
la-integral-definida:@0.736082:0.673176:0.846656:0.673176:0.846656:0.659547:0.736082:0.659547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∑:@0.222148:0.122945:0.237526:0.122945:0.237526:0.097123:0.222148:0.097123:0.000000
n:@0.227584:0.103578:0.233042:0.103578:0.233042:0.093977:0.227584:0.093977:0.000000
j:@0.223563:0.128639:0.225809:0.128639:0.225809:0.119038:0.223563:0.119038:0.000000
=0:@0.225809:0.128572:0.237063:0.128572:0.237063:0.118954:0.225809:0.118954:0.000000:0.000000
∑:@0.279674:0.165951:0.295052:0.165951:0.295052:0.140129:0.279674:0.140129:0.000000
n:@0.285108:0.146584:0.290567:0.146584:0.290567:0.136983:0.285108:0.136983:0.000000
j:@0.281087:0.171645:0.283334:0.171645:0.283334:0.162044:0.281087:0.162044:0.000000
=0:@0.283334:0.171578:0.294588:0.171578:0.294588:0.161960:0.283334:0.161960:0.000000:0.000000
3:@0.342936:0.113091:0.351432:0.113091:0.351432:0.096593:0.342936:0.096593:0.000000
2:@0.342936:0.129430:0.351432:0.129430:0.351432:0.112932:0.342936:0.112932:0.000000
n n:@0.332216:0.193428:0.356895:0.193428:0.356895:0.176959:0.332216:0.176959:0.000000:0.000000:0.000000
(  + 1) (1 + 2 ):@0.341579:0.193312:0.451930:0.193312:0.451930:0.176814:0.341579:0.176814:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
n:@0.436614:0.193428:0.445977:0.193428:0.445977:0.176959:0.436614:0.176959:0.000000
6:@0.387815:0.209651:0.396311:0.209651:0.396311:0.193153:0.387815:0.193153:0.000000
U:@0.498812:0.773558:0.518503:0.773558:0.518503:0.747736:0.498812:0.747736:0.000000
n:@0.506397:0.752934:0.511856:0.752934:0.511856:0.743333:0.506397:0.743333:0.000000
j:@0.502376:0.777995:0.504623:0.777995:0.504623:0.768394:0.502376:0.768394:0.000000
=1:@0.504623:0.777927:0.515877:0.777927:0.515877:0.768309:0.504623:0.768309:0.000000:0.000000
b a:@0.460447:0.893953:0.497475:0.893953:0.497475:0.877484:0.460447:0.877484:0.000000:0.000000:0.000000
 – :@0.469714:0.893837:0.488497:0.893837:0.488497:0.877340:0.469714:0.877340:0.000000:0.000000:0.000000
n:@0.474280:0.910292:0.483643:0.910292:0.483643:0.893823:0.474280:0.893823:0.000000
∫:@0.654815:0.391193:0.661135:0.391193:0.663331:0.367628:0.657010:0.367628:0.000000
b:@0.664522:0.373746:0.669384:0.373746:0.669384:0.365105:0.664522:0.365105:0.000000
a:@0.661307:0.393259:0.666018:0.393259:0.666018:0.384618:0.661307:0.384618:0.000000
∫:@0.654815:0.494222:0.661135:0.494222:0.663331:0.470657:0.657010:0.470657:0.000000
b:@0.664522:0.476776:0.669384:0.476776:0.669384:0.468135:0.664522:0.468135:0.000000
a:@0.661307:0.496289:0.666018:0.496289:0.666018:0.487648:0.661307:0.487648:0.000000
∫:@0.725248:0.494222:0.731569:0.494222:0.733765:0.470657:0.727444:0.470657:0.000000
b:@0.734954:0.476776:0.739816:0.476776:0.739816:0.468135:0.734954:0.468135:0.000000
a:@0.731739:0.496289:0.736450:0.496289:0.736450:0.487648:0.731739:0.487648:0.000000
∫:@0.721047:0.391193:0.727367:0.391193:0.729563:0.367628:0.723242:0.367628:0.000000
c:@0.731298:0.373746:0.735069:0.373746:0.735069:0.365105:0.731298:0.365105:0.000000
b:@0.727467:0.393259:0.732329:0.393259:0.732329:0.384618:0.727467:0.384618:0.000000
∫:@0.787277:0.391193:0.793598:0.391193:0.795794:0.367628:0.789473:0.367628:0.000000
c:@0.797529:0.373746:0.801299:0.373746:0.801299:0.365105:0.797529:0.365105:0.000000
a:@0.793769:0.393259:0.798479:0.393259:0.798479:0.384618:0.793769:0.384618:0.000000
p:@0.108233:0.530268:0.119713:0.530268:0.119713:0.520243:0.108233:0.520243:0.000000
 :@0.119714:0.530976:0.122595:0.530976:0.122595:0.519499:0.119714:0.519499:0.000000
Figura 6.3.:@0.122595:0.530976:0.171164:0.530976:0.171164:0.519499:0.122595:0.519499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.107863:0.511348:0.114363:0.511348:0.114363:0.497027:0.107863:0.497027:0.000000
0:@0.114362:0.514097:0.118669:0.514097:0.118669:0.505734:0.114362:0.505734:0.000000
 = :@0.118669:0.511248:0.135271:0.511248:0.135271:0.496902:0.118669:0.496902:0.000000:0.000000:0.000000
a:@0.135271:0.511348:0.143078:0.511348:0.143078:0.497027:0.135271:0.497027:0.000000
b x:@0.559525:0.511348:0.590685:0.511348:0.590685:0.497027:0.559525:0.497027:0.000000:0.000000:0.000000
 = :@0.567583:0.511248:0.584185:0.511248:0.584185:0.496902:0.567583:0.496902:0.000000:0.000000:0.000000
n:@0.590586:0.514156:0.595333:0.514156:0.595333:0.505807:0.590586:0.505807:0.000000
x:@0.190487:0.511348:0.196987:0.511348:0.196987:0.497027:0.190487:0.497027:0.000000
1:@0.196987:0.514097:0.201294:0.514097:0.201294:0.505734:0.196987:0.505734:0.000000
x:@0.243621:0.511348:0.250121:0.511348:0.250121:0.497027:0.243621:0.497027:0.000000
2:@0.250121:0.514097:0.254428:0.514097:0.254428:0.505734:0.250121:0.505734:0.000000
x:@0.341259:0.511348:0.347759:0.511348:0.347759:0.497027:0.341259:0.497027:0.000000
3:@0.347759:0.514097:0.352066:0.514097:0.352066:0.505734:0.347759:0.505734:0.000000
x:@0.385291:0.511348:0.391791:0.511348:0.391791:0.497027:0.385291:0.497027:0.000000
4:@0.391791:0.514097:0.396098:0.514097:0.396098:0.505734:0.391791:0.505734:0.000000
x:@0.428847:0.511348:0.435347:0.511348:0.435347:0.497027:0.428847:0.497027:0.000000
5:@0.435347:0.514097:0.439654:0.514097:0.439654:0.505734:0.435347:0.505734:0.000000
x:@0.537012:0.511348:0.543512:0.511348:0.543512:0.497027:0.537012:0.497027:0.000000
6:@0.543511:0.514097:0.547818:0.514097:0.547818:0.505734:0.543511:0.505734:0.000000
p:@0.651765:0.605901:0.663245:0.605901:0.663245:0.595876:0.651765:0.595876:0.000000
 :@0.663245:0.606609:0.666126:0.606609:0.666126:0.595132:0.663245:0.595132:0.000000
Ilustración gráfica del concepto :@0.666126:0.606609:0.823961:0.606609:0.823961:0.595132:0.666126:0.595132:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de integral definida:@0.651773:0.618679:0.747247:0.618679:0.747247:0.607202:0.651773:0.607202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Competencia :@0.684804:0.709291:0.782426:0.709291:0.782426:0.693818:0.684804:0.693818:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
socioemocional:@0.684804:0.721859:0.795179:0.721859:0.795179:0.706386:0.684804:0.706386:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Analiza:@0.685042:0.746531:0.734733:0.746531:0.734733:0.731270:0.685042:0.731270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 esta frase y :@0.734733:0.746333:0.813236:0.746333:0.813236:0.731270:0.734733:0.731270:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
escribe:@0.638498:0.762373:0.686062:0.762373:0.686062:0.747112:0.638498:0.747112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 un ejemplo de una :@0.686062:0.762175:0.816261:0.762175:0.816261:0.747112:0.686062:0.747112:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
situación en la que la podrías :@0.638498:0.778017:0.830105:0.778017:0.830105:0.762954:0.638498:0.762954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
aplicar.:@0.638498:0.793859:0.682720:0.793859:0.682720:0.778796:0.638498:0.778796:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
\Estar preparado es importante:@0.638498:0.820513:0.847413:0.820513:0.847413:0.805450:0.638498:0.805450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
saber esperar lo es aún más, :@0.638498:0.836355:0.821855:0.836355:0.821855:0.821292:0.638498:0.821292:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
pero aprovechar el momento :@0.638498:0.852197:0.832972:0.852197:0.832972:0.837134:0.638498:0.837134:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
adecuado es la clave de la vida.\:@0.638498:0.868039:0.842734:0.868039:0.842734:0.852976:0.638498:0.852976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Arthur Schnitzler:@0.750404:0.881138:0.846655:0.881138:0.846655:0.868227:0.750404:0.868227:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000