189:@0.916858:0.966074:0.945034:0.966074:0.945034:0.949450:0.916858:0.949450:0.000000:0.000000:0.000000 La suma::@0.108233:0.096194:0.169901:0.096194:0.169901:0.079697:0.108233:0.079697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c h:@0.275783:0.113661:0.297322:0.113661:0.297322:0.097192:0.275783:0.097192:0.000000:0.000000:0.000000 1 1:@0.282969:0.116823:0.302276:0.116823:0.302276:0.107205:0.282969:0.107205:0.000000:0.000000:0.000000 + :@0.302276:0.113545:0.321368:0.113545:0.321368:0.097047:0.302276:0.097047:0.000000:0.000000:0.000000 c h:@0.321368:0.113661:0.342907:0.113661:0.342907:0.097192:0.321368:0.097192:0.000000:0.000000:0.000000 2 2:@0.328552:0.116823:0.347861:0.116823:0.347861:0.107205:0.328552:0.107205:0.000000:0.000000:0.000000 + … + :@0.347861:0.113545:0.401091:0.113545:0.401091:0.097047:0.347861:0.097047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c h:@0.401091:0.113661:0.422913:0.113661:0.422913:0.097192:0.401091:0.097192:0.000000:0.000000:0.000000 n n:@0.408121:0.116890:0.428218:0.116890:0.428218:0.107289:0.408121:0.107289:0.000000:0.000000:0.000000 se expresa como :@0.108233:0.145152:0.247249:0.145152:0.247249:0.128655:0.108233:0.128655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ch:@0.247249:0.145268:0.266014:0.145268:0.266014:0.128799:0.247249:0.128799:0.000000:0.000000 j j:@0.254435:0.148498:0.268183:0.148498:0.268183:0.138896:0.254435:0.138896:0.000000:0.000000:0.000000 o también así::@0.268183:0.145152:0.370961:0.145152:0.370961:0.128655:0.268183:0.128655:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( – :@0.154403:0.173188:0.219006:0.173195:0.219006:0.156697:0.154403:0.156691:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c x:@0.175113:0.173304:0.197976:0.173311:0.197976:0.156842:0.175113:0.156835:0.000000:0.000000:0.000000 j:@0.182302:0.176541:0.184548:0.176541:0.184548:0.166939:0.182302:0.166939:0.000000 j:@0.197976:0.176541:0.200222:0.176541:0.200222:0.166939:0.197976:0.166939:0.000000 x:@0.219006:0.173311:0.226481:0.173311:0.226481:0.156842:0.219006:0.156842:0.000000 j:@0.226480:0.176541:0.228726:0.176541:0.228726:0.166939:0.226480:0.166939:0.000000 –1:@0.228726:0.176473:0.239801:0.176473:0.239801:0.166855:0.228726:0.166855:0.000000:0.000000 ), que se lee “suma de = 1 hasta de :@0.239801:0.173195:0.509317:0.173195:0.509317:0.156697:0.239801:0.156697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.396251:0.173311:0.400104:0.173311:0.400104:0.156842:0.396251:0.156842:0.000000 n:@0.473813:0.173311:0.483175:0.173311:0.483175:0.156842:0.473813:0.156842:0.000000 ch:@0.509317:0.173311:0.528083:0.173311:0.528083:0.156842:0.509317:0.156842:0.000000:0.000000 j j:@0.516502:0.176541:0.530253:0.176541:0.530253:0.166939:0.516502:0.166939:0.000000:0.000000:0.000000 ” o:@0.530251:0.173195:0.549593:0.173195:0.549593:0.156697:0.530251:0.156697:0.000000:0.000000:0.000000 “de ( – :@0.108226:0.201231:0.179016:0.201238:0.179016:0.184740:0.108226:0.184733:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c x:@0.135121:0.201347:0.157987:0.201354:0.157987:0.184885:0.135121:0.184878:0.000000:0.000000:0.000000 j:@0.142312:0.204582:0.144559:0.204582:0.144559:0.194981:0.142312:0.194981:0.000000 j:@0.157986:0.204582:0.160232:0.204582:0.160232:0.194981:0.157986:0.194981:0.000000 x:@0.179016:0.201354:0.186491:0.201354:0.186491:0.184885:0.179016:0.184885:0.000000 j:@0.186490:0.204582:0.188737:0.204582:0.188737:0.194981:0.186490:0.194981:0.000000 –1:@0.188737:0.204515:0.199811:0.204515:0.199811:0.194896:0.188737:0.194896:0.000000:0.000000 )”. Así, :@0.199812:0.201238:0.245933:0.201238:0.245933:0.184740:0.199812:0.184740:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) = :@0.146177:0.234436:0.238573:0.234436:0.238573:0.217938:0.146177:0.217938:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x dx:@0.162745:0.234551:0.202913:0.234551:0.202913:0.218083:0.162745:0.218083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c h:@0.238573:0.234551:0.260105:0.234546:0.260105:0.218078:0.238573:0.218083:0.000000:0.000000:0.000000 1 1:@0.245750:0.237707:0.265058:0.237707:0.265058:0.228089:0.245750:0.228089:0.000000:0.000000:0.000000 = ( – :@0.265057:0.234431:0.344607:0.234431:0.344607:0.217933:0.265057:0.217933:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c x:@0.300717:0.234546:0.323578:0.234546:0.323578:0.218078:0.300717:0.218078:0.000000:0.000000:0.000000 j:@0.307903:0.237775:0.310150:0.237775:0.310150:0.228174:0.307903:0.228174:0.000000 j:@0.323577:0.237775:0.325823:0.237775:0.325823:0.228174:0.323577:0.228174:0.000000 x:@0.344607:0.234546:0.352082:0.234546:0.352082:0.218078:0.344607:0.218078:0.000000 j:@0.352081:0.237775:0.354327:0.237775:0.354327:0.228174:0.352081:0.228174:0.000000 –1:@0.354327:0.237707:0.365402:0.237707:0.365402:0.228089:0.354327:0.228089:0.000000:0.000000 ) = :@0.365401:0.234431:0.390446:0.234431:0.390446:0.217933:0.365401:0.217933:0.000000:0.000000:0.000000:0.000000 c h:@0.390446:0.234546:0.411986:0.234546:0.411986:0.218078:0.390446:0.218078:0.000000:0.000000:0.000000 1 1:@0.397631:0.237707:0.416939:0.237707:0.416939:0.228089:0.397631:0.228089:0.000000:0.000000:0.000000 + :@0.416940:0.234431:0.436031:0.234431:0.436031:0.217933:0.416940:0.217933:0.000000:0.000000:0.000000 c h:@0.436031:0.234546:0.457571:0.234546:0.457571:0.218078:0.436031:0.218078:0.000000:0.000000:0.000000 2 2:@0.443216:0.237707:0.462524:0.237707:0.462524:0.228089:0.443216:0.228089:0.000000:0.000000:0.000000 + … + :@0.462523:0.234431:0.515753:0.234431:0.515753:0.217933:0.462523:0.217933:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c h:@0.515753:0.234546:0.537577:0.234546:0.537577:0.218078:0.515753:0.218078:0.000000:0.000000:0.000000 n n:@0.522785:0.237775:0.542881:0.237775:0.542881:0.228174:0.522785:0.228174:0.000000:0.000000:0.000000 =:@0.542881:0.234431:0.557831:0.234431:0.557831:0.217933:0.542881:0.217933:0.000000:0.000000 c x:@0.206837:0.262582:0.232403:0.262589:0.232403:0.246120:0.206837:0.246114:0.000000:0.000000:0.000000 1:@0.214021:0.265750:0.218974:0.265750:0.218974:0.256132:0.214021:0.256132:0.000000 ( – ) + ( – ) + … + ( – :@0.218975:0.262474:0.464566:0.262474:0.464566:0.245976:0.218975:0.245976:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.232402:0.265750:0.237355:0.265750:0.237355:0.256132:0.232402:0.256132:0.000000 x:@0.256137:0.262589:0.263612:0.262589:0.263612:0.246120:0.256137:0.246120:0.000000 0:@0.263613:0.265750:0.268566:0.265750:0.268566:0.256132:0.263613:0.256132:0.000000 c x:@0.293610:0.262589:0.319177:0.262589:0.319177:0.246120:0.293610:0.246120:0.000000:0.000000:0.000000 2:@0.300795:0.265750:0.305748:0.265750:0.305748:0.256132:0.300795:0.256132:0.000000 2:@0.319176:0.265750:0.324129:0.265750:0.324129:0.256132:0.319176:0.256132:0.000000 x:@0.342913:0.262589:0.350388:0.262589:0.350388:0.246120:0.342913:0.246120:0.000000 1:@0.350387:0.265750:0.355340:0.265750:0.355340:0.256132:0.350387:0.256132:0.000000 c x:@0.414524:0.262589:0.440441:0.262589:0.440441:0.246120:0.414524:0.246120:0.000000:0.000000:0.000000 n:@0.421553:0.265818:0.427012:0.265818:0.427012:0.256216:0.421553:0.256216:0.000000 n:@0.440324:0.265818:0.445783:0.265818:0.445783:0.256216:0.440324:0.256216:0.000000 x:@0.464566:0.262589:0.472041:0.262589:0.472041:0.246120:0.464566:0.246120:0.000000 n:@0.471926:0.265818:0.477385:0.265818:0.477385:0.256216:0.471926:0.256216:0.000000 –1:@0.477385:0.265750:0.488459:0.265750:0.488459:0.256132:0.477385:0.256132:0.000000:0.000000 ).:@0.488457:0.262474:0.497165:0.262474:0.497165:0.245976:0.488457:0.245976:0.000000:0.000000 Notemos que el cálculo de se reduce a calcular la suma::@0.108238:0.297175:0.527236:0.297175:0.527236:0.280677:0.108238:0.280677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.319537:0.297291:0.323834:0.297291:0.323834:0.280822:0.319537:0.280822:0.000000 c h:@0.108238:0.321770:0.129773:0.321769:0.129773:0.305300:0.108238:0.305301:0.000000:0.000000:0.000000 1 1:@0.115419:0.324931:0.134726:0.324931:0.134726:0.315313:0.115419:0.315313:0.000000:0.000000:0.000000 + :@0.134727:0.321653:0.153819:0.321653:0.153819:0.305156:0.134727:0.305156:0.000000:0.000000:0.000000 c h:@0.153819:0.321769:0.175358:0.321769:0.175358:0.305300:0.153819:0.305300:0.000000:0.000000:0.000000 2 2:@0.161003:0.324931:0.180311:0.324931:0.180311:0.315313:0.161003:0.315313:0.000000:0.000000:0.000000 + … + :@0.180310:0.321653:0.233540:0.321653:0.233540:0.305156:0.180310:0.305156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c h:@0.233540:0.321769:0.255364:0.321769:0.255364:0.305300:0.233540:0.305300:0.000000:0.000000:0.000000 n n:@0.240572:0.324999:0.260669:0.324999:0.260669:0.315398:0.240572:0.315398:0.000000:0.000000:0.000000 que requiere únicamente de los elementos :@0.260668:0.321653:0.571068:0.321653:0.571068:0.305156:0.260668:0.305156:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 básicos de suma y multiplicación de números reales.:@0.108241:0.339004:0.478514:0.339004:0.478514:0.322507:0.108241:0.322507:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sean , , tales que < y la función real definida en el intervalo :@0.108241:0.373706:0.599995:0.373706:0.599995:0.357208:0.108241:0.357208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.145231:0.373821:0.169563:0.373821:0.169563:0.357353:0.145231:0.357353:0.000000:0.000000:0.000000 :@0.172869:0.373187:0.187521:0.373187:0.187521:0.359814:0.172869:0.359814:0.000000 :@0.190849:0.372619:0.204154:0.372619:0.204154:0.359757:0.190849:0.359757:0.000000 a b f:@0.276379:0.373821:0.330881:0.373821:0.330881:0.357353:0.276379:0.357353:0.000000:0.000000:0.000000:0.000000:0.000000 cerrado [ , ]. En el cálculo de integrales definidas de funciones:@0.108232:0.391056:0.556664:0.391056:0.556664:0.374559:0.108232:0.374559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.172617:0.391172:0.197758:0.391172:0.197758:0.374703:0.172617:0.374703:0.000000:0.000000:0.000000 escalonadas se introdujo el símbolo ( ) que se lee “integral:@0.108232:0.415535:0.568572:0.415535:0.568572:0.399038:0.108232:0.399038:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x dx:@0.386342:0.415651:0.431480:0.415651:0.431480:0.399182:0.386342:0.399182:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 definida desde hasta de la función :@0.108232:0.440014:0.382236:0.440014:0.382236:0.423517:0.108232:0.423517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.216807:0.440130:0.225785:0.440130:0.225785:0.423661:0.216807:0.423661:0.000000 b:@0.271906:0.440130:0.281173:0.440130:0.281173:0.423661:0.271906:0.423661:0.000000 escalonada:@0.382236:0.440231:0.464304:0.440231:0.464304:0.423517:0.382236:0.423517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ”.:@0.464312:0.440014:0.484637:0.440014:0.484637:0.423517:0.464312:0.423517:0.000000:0.000000:0.000000:0.000000 p:@0.468454:0.440130:0.477721:0.440130:0.477721:0.423661:0.468454:0.423661:0.000000 Definición:@0.108232:0.475179:0.188316:0.475179:0.188316:0.458233:0.108232:0.458233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 i):@0.108232:0.492284:0.118770:0.492284:0.118770:0.475569:0.108232:0.475569:0.000000:0.000000 Se dice que ( ) es una sucesión de funciones escalonadas de-:@0.118769:0.492067:0.595810:0.492067:0.595810:0.475569:0.118769:0.475569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.230506:0.492182:0.239773:0.492182:0.239773:0.475714:0.230506:0.475714:0.000000 n:@0.239709:0.495411:0.245168:0.495411:0.245168:0.485810:0.239709:0.485810:0.000000 finidas en [ , ], si y solo si para cada :@0.131984:0.509417:0.440828:0.509417:0.440828:0.492920:0.131984:0.492920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.212609:0.509533:0.238944:0.509533:0.238944:0.493064:0.212609:0.493064:0.000000:0.000000:0.000000 n:@0.407342:0.509533:0.416705:0.509533:0.416705:0.493064:0.407342:0.493064:0.000000 :@0.422032:0.508899:0.436685:0.508899:0.436685:0.495526:0.422032:0.495526:0.000000 Z:@0.442038:0.508331:0.454329:0.508331:0.454329:0.495468:0.442038:0.495468:0.000000 +:@0.454329:0.501807:0.460630:0.501807:0.460630:0.492189:0.454329:0.492189:0.000000 , es una función :@0.460630:0.509417:0.599921:0.509417:0.599921:0.492920:0.460630:0.492920:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.468740:0.509533:0.478007:0.509533:0.478007:0.493064:0.468740:0.493064:0.000000 n:@0.477945:0.512762:0.483404:0.512762:0.483404:0.503160:0.477945:0.503160:0.000000 escalonada en [ , ]. Esto es, ([ , ]).:@0.131968:0.526768:0.433789:0.526768:0.433789:0.510271:0.131968:0.510271:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.242645:0.526884:0.267786:0.526884:0.267786:0.510415:0.242645:0.510415:0.000000:0.000000:0.000000 p:@0.336484:0.526884:0.345751:0.526884:0.345751:0.510415:0.336484:0.510415:0.000000 n:@0.345700:0.530112:0.351159:0.530112:0.351159:0.520511:0.345700:0.520511:0.000000 :@0.355301:0.526250:0.369953:0.526250:0.369953:0.512876:0.355301:0.512876:0.000000 ε:@0.374095:0.534355:0.382277:0.534355:0.382277:0.515356:0.374095:0.515356:0.000000 a b:@0.394083:0.526884:0.419225:0.526884:0.419225:0.510415:0.394083:0.510415:0.000000:0.000000:0.000000 ii):@0.108226:0.561687:0.123021:0.561687:0.123021:0.544972:0.108226:0.544972:0.000000:0.000000:0.000000 Sea una función real definida en [ , ]. Se dice que la sucesión de :@0.123022:0.561470:0.599895:0.561470:0.599895:0.544972:0.123022:0.544972:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.159954:0.561585:0.164250:0.561585:0.164250:0.545117:0.159954:0.545117:0.000000 a b:@0.375877:0.561585:0.400750:0.561585:0.400750:0.545117:0.375877:0.545117:0.000000:0.000000:0.000000 funciones escalonadas ( ) converge a , si y solo si se verifica::@0.131961:0.578821:0.563693:0.578821:0.563693:0.562323:0.131961:0.562323:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.300975:0.578936:0.310242:0.578936:0.310242:0.562467:0.300975:0.562467:0.000000 n:@0.310197:0.582165:0.315655:0.582165:0.315655:0.572563:0.310197:0.572563:0.000000 f:@0.406259:0.578936:0.410555:0.578936:0.410555:0.562467:0.406259:0.562467:0.000000 lím ( ) = ( ), [ , ].:@0.263734:0.596171:0.464003:0.596171:0.464003:0.579674:0.263734:0.579674:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x:@0.290397:0.596287:0.318502:0.596287:0.318502:0.579818:0.290397:0.579818:0.000000:0.000000:0.000000 n:@0.299616:0.599515:0.305074:0.599515:0.305074:0.589914:0.299616:0.589914:0.000000 f x:@0.343546:0.596287:0.361270:0.596287:0.361270:0.579818:0.343546:0.579818:0.000000:0.000000:0.000000 ∀:@0.382403:0.603758:0.393975:0.603758:0.393975:0.584759:0.382403:0.584759:0.000000 x:@0.393982:0.596287:0.401457:0.596287:0.401457:0.579818:0.393982:0.579818:0.000000 :@0.405598:0.595653:0.420251:0.595653:0.420251:0.582279:0.405598:0.582279:0.000000 a b:@0.430250:0.596287:0.455391:0.596287:0.455391:0.579818:0.430250:0.579818:0.000000:0.000000:0.000000 :@0.108231:0.613522:0.116515:0.613522:0.116515:0.597024:0.108231:0.597024:0.000000:0.000000 Sea una función real definida en el intervalo [ , ].:@0.108231:0.630873:0.470472:0.630873:0.470472:0.614375:0.108231:0.614375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.136494:0.630988:0.140790:0.630988:0.140790:0.614520:0.136494:0.614520:0.000000 a b:@0.436719:0.630988:0.461861:0.630988:0.461861:0.614520:0.436719:0.614520:0.000000:0.000000:0.000000 El símbolo ( ) se lee “integral definida desde hasta de la:@0.108231:0.655352:0.564752:0.655352:0.564752:0.638854:0.108231:0.638854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x dx:@0.198795:0.655467:0.243934:0.655467:0.243934:0.638999:0.198795:0.638999:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.462591:0.655467:0.471568:0.655467:0.471568:0.638999:0.462591:0.638999:0.000000 b:@0.517689:0.655467:0.526956:0.655467:0.526956:0.638999:0.517689:0.638999:0.000000 función real dada como ( ) por ”. La integral de funciones reales :@0.108231:0.679831:0.599898:0.679831:0.599898:0.663333:0.108231:0.663333:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.287822:0.679946:0.305546:0.679946:0.305546:0.663478:0.287822:0.663478:0.000000:0.000000:0.000000 dx:@0.348084:0.679946:0.364575:0.679946:0.364575:0.663478:0.348084:0.663478:0.000000:0.000000 que se definen a continuación se conoce en la literatura como :@0.108231:0.697182:0.560695:0.697182:0.560695:0.680684:0.108231:0.680684:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 inte-:@0.561369:0.697398:0.595758:0.697398:0.595758:0.680684:0.561369:0.680684:0.000000:0.000000:0.000000:0.000000:0.000000 gral de Riemann:@0.108231:0.714749:0.227982:0.714749:0.227982:0.698035:0.108231:0.698035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Para facilitar la comprensión, la siguiente definición :@0.227982:0.714532:0.599896:0.714532:0.599896:0.698035:0.227982:0.698035:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de integral definida es una simplificación de la definición de integral :@0.108231:0.731883:0.599952:0.731883:0.599952:0.715385:0.108231:0.715385:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de Riemann a una clase de funciones continuas .:@0.108231:0.749234:0.456062:0.749234:0.456062:0.732736:0.108231:0.732736:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.449011:0.749350:0.453307:0.749350:0.453307:0.732881:0.449011:0.732881:0.000000 Definición :@0.108231:0.784398:0.195098:0.784398:0.195098:0.767452:0.108231:0.767452:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sea una función real definida en el intervalo [ , ]. Se :@0.188317:0.783935:0.599919:0.783935:0.599919:0.767438:0.188317:0.767438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.226327:0.784051:0.230624:0.784051:0.230624:0.767582:0.226327:0.767582:0.000000 a b:@0.538573:0.784051:0.565184:0.784051:0.565184:0.767582:0.538573:0.767582:0.000000:0.000000:0.000000 dice que es:@0.108231:0.801286:0.195694:0.801286:0.195694:0.784788:0.108231:0.784788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.172884:0.801402:0.177180:0.801402:0.177180:0.784933:0.172884:0.784933:0.000000 integrable en [ , ], que se escribe ( ):@0.108231:0.825765:0.392795:0.825765:0.392795:0.809267:0.108231:0.809267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.210740:0.825881:0.235881:0.825881:0.235881:0.809412:0.210740:0.809412:0.000000:0.000000:0.000000 f x dx,:@0.369118:0.825881:0.412253:0.825881:0.412253:0.809412:0.369118:0.809412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 si y solo si existe una:@0.412256:0.825765:0.561329:0.825765:0.561329:0.809267:0.412256:0.809267:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sucesión de funciones escalonadas ( ) definidas en [ , ], tales que: :@0.108231:0.850244:0.597742:0.850243:0.597742:0.833745:0.108231:0.833746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.364324:0.850360:0.373591:0.850360:0.373591:0.833891:0.364324:0.833891:0.000000 n:@0.373529:0.853587:0.378988:0.853587:0.378988:0.843986:0.373529:0.843986:0.000000 a b:@0.485196:0.850359:0.510337:0.850359:0.510337:0.833890:0.485196:0.833890:0.000000:0.000000:0.000000 lím ( ) = ( ), [ , ],:@0.264938:0.874722:0.465201:0.874721:0.465201:0.858224:0.264938:0.858224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x:@0.291601:0.874838:0.319699:0.874837:0.319699:0.858368:0.291601:0.858369:0.000000:0.000000:0.000000 n:@0.300812:0.878067:0.306271:0.878067:0.306271:0.868465:0.300812:0.868465:0.000000 f x:@0.344744:0.874837:0.362468:0.874837:0.362468:0.858368:0.344744:0.858368:0.000000:0.000000:0.000000 ∀:@0.383599:0.882308:0.395171:0.882308:0.395171:0.863309:0.383599:0.863309:0.000000 x:@0.395180:0.874837:0.402655:0.874837:0.402655:0.858368:0.395180:0.858368:0.000000 :@0.406796:0.874203:0.421448:0.874203:0.421448:0.860829:0.406796:0.860829:0.000000 a b:@0.431448:0.874837:0.456589:0.874837:0.456589:0.858368:0.431448:0.858368:0.000000:0.000000:0.000000 lím ( ) existe.:@0.264938:0.906329:0.389032:0.906329:0.389032:0.889831:0.264938:0.889831:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x:@0.308170:0.906444:0.336266:0.906444:0.336266:0.889975:0.308170:0.889975:0.000000:0.000000:0.000000 n:@0.317380:0.909673:0.322839:0.909673:0.322839:0.900071:0.317380:0.900071:0.000000 En tal caso, ( ) = lím ( ).:@0.108223:0.941030:0.347029:0.941030:0.347029:0.924532:0.108223:0.924532:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x dx:@0.207726:0.941146:0.247894:0.941146:0.247894:0.924677:0.207726:0.924677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p x:@0.310219:0.941146:0.338321:0.941145:0.338321:0.924677:0.310219:0.924677:0.000000:0.000000:0.000000 n:@0.319434:0.944375:0.324892:0.944375:0.324892:0.934773:0.319434:0.934773:0.000000 Recuerda que…:@0.684804:0.121000:0.794564:0.121000:0.794564:0.105527:0.684804:0.105527:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Primer teorema funda-:@0.685042:0.150049:0.846215:0.150049:0.846215:0.134577:0.685042:0.134577:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 mental del cálculo integral:@0.638498:0.165891:0.825512:0.165891:0.825512:0.150419:0.638498:0.150419:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si es una función continua en :@0.638498:0.181311:0.841765:0.181311:0.841765:0.166248:0.638498:0.166248:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.653063:0.181417:0.656985:0.181417:0.656985:0.166380:0.653063:0.166380:0.000000 [ , ], entonces la función :@0.638498:0.197153:0.820395:0.197153:0.820395:0.182090:0.638498:0.182090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.643846:0.197259:0.666801:0.197259:0.666801:0.182222:0.643846:0.182222:0.000000:0.000000:0.000000 F:@0.809718:0.197259:0.816613:0.197259:0.816613:0.182222:0.809718:0.182222:0.000000 definida por:@0.638498:0.212995:0.718355:0.212995:0.718355:0.197932:0.638498:0.197932:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F x:@0.638498:0.237854:0.657654:0.237854:0.657654:0.222817:0.638498:0.222817:0.000000:0.000000:0.000000 ( ) = ( ):@0.645394:0.237748:0.711831:0.237748:0.711831:0.222685:0.645394:0.222685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f t dt :@0.691866:0.237854:0.732851:0.237854:0.732851:0.222817:0.691866:0.222817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 es continua en:@0.732851:0.237748:0.827695:0.237748:0.827695:0.222685:0.732851:0.222685:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [ , ] y satisface que '( ) = ( ).:@0.638498:0.260719:0.842138:0.260719:0.842138:0.245656:0.638498:0.245656:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.643846:0.260825:0.666801:0.260825:0.666801:0.245788:0.643846:0.245788:0.000000:0.000000:0.000000 F x:@0.772638:0.260825:0.795137:0.260825:0.795137:0.245788:0.772638:0.245788:0.000000:0.000000:0.000000 f x:@0.818004:0.260825:0.834187:0.260825:0.834187:0.245788:0.818004:0.245788:0.000000:0.000000:0.000000 Segundo teorema fundamen-:@0.638498:0.292825:0.844140:0.292825:0.844140:0.277353:0.638498:0.277353:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tal del cálculo integral:@0.638498:0.308667:0.794200:0.308667:0.794200:0.293195:0.638498:0.293195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Si es una función continua en :@0.638498:0.339929:0.841765:0.339929:0.841765:0.324866:0.638498:0.324866:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.653063:0.340035:0.656985:0.340035:0.656985:0.324998:0.653063:0.324998:0.000000 [ , ], entonces :@0.638498:0.355771:0.741312:0.355771:0.741312:0.340708:0.638498:0.340708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.643846:0.355877:0.666801:0.355877:0.666801:0.340840:0.643846:0.340840:0.000000:0.000000:0.000000 ( ):@0.638498:0.380524:0.675244:0.380524:0.675244:0.365461:0.638498:0.365461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x dx = F b:@0.653626:0.380630:0.728594:0.380630:0.728594:0.365593:0.653626:0.365593:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) – ( ),:@0.714698:0.380524:0.779658:0.380524:0.779658:0.365461:0.714698:0.365461:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F a:@0.751180:0.380630:0.771708:0.380630:0.771708:0.365593:0.751180:0.365593:0.000000:0.000000:0.000000 donde es cualquier primitiva :@0.638498:0.403495:0.837916:0.403495:0.837916:0.388432:0.638498:0.388432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 F:@0.685094:0.403601:0.691990:0.403601:0.691990:0.388564:0.685094:0.388564:0.000000 de en el intervalo [ , ].:@0.638498:0.419337:0.797757:0.419337:0.797757:0.404274:0.638498:0.404274:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.658586:0.419443:0.662509:0.419443:0.662509:0.404406:0.658586:0.404406:0.000000 a b:@0.766939:0.419443:0.789894:0.419443:0.789894:0.404406:0.766939:0.404406:0.000000:0.000000:0.000000 ∑:@0.230946:0.146867:0.246325:0.146867:0.246325:0.121044:0.230946:0.121044:0.000000 n:@0.236382:0.127501:0.241841:0.127501:0.241841:0.117900:0.236382:0.117900:0.000000 j:@0.232361:0.152562:0.234608:0.152562:0.234608:0.142961:0.232361:0.142961:0.000000 =1:@0.234608:0.152494:0.245862:0.152494:0.245862:0.142876:0.234608:0.142876:0.000000:0.000000 ∑:@0.159824:0.176948:0.175202:0.176948:0.175202:0.151125:0.159824:0.151125:0.000000 n:@0.165258:0.157580:0.170717:0.157580:0.170717:0.147979:0.165258:0.147979:0.000000 j:@0.161237:0.182642:0.163484:0.182642:0.163484:0.173040:0.161237:0.173040:0.000000 =1:@0.163484:0.182574:0.174738:0.182574:0.174738:0.172956:0.163484:0.172956:0.000000:0.000000 ∑:@0.222702:0.237561:0.238081:0.237561:0.238081:0.211738:0.222702:0.211738:0.000000 n:@0.228137:0.218194:0.233595:0.218194:0.233595:0.208592:0.228137:0.208592:0.000000 j:@0.224116:0.243255:0.226362:0.243255:0.226362:0.233653:0.224116:0.233653:0.000000 =1:@0.226362:0.243187:0.237616:0.243187:0.237616:0.233569:0.226362:0.233569:0.000000:0.000000 ∑:@0.284686:0.237561:0.300065:0.237561:0.300065:0.211738:0.284686:0.211738:0.000000 n:@0.290121:0.218194:0.295579:0.218194:0.295579:0.208592:0.290121:0.208592:0.000000 j:@0.286100:0.243255:0.288346:0.243255:0.288346:0.233653:0.286100:0.233653:0.000000 =1:@0.288346:0.243187:0.299600:0.243187:0.299600:0.233569:0.288346:0.233569:0.000000:0.000000 ∫:@0.148208:0.238965:0.155231:0.238965:0.157671:0.212782:0.150648:0.212782:0.000000 b:@0.158991:0.219580:0.164394:0.219580:0.164394:0.209979:0.158991:0.209979:0.000000 a:@0.155420:0.241261:0.160653:0.241261:0.160653:0.231660:0.155420:0.231660:0.000000 ∫:@0.305545:0.302131:0.312568:0.302131:0.315008:0.275947:0.307985:0.275947:0.000000 b:@0.316328:0.282745:0.321730:0.282745:0.321730:0.273143:0.316328:0.273143:0.000000 a:@0.312756:0.304426:0.317990:0.304426:0.317990:0.294824:0.312756:0.294824:0.000000 ∫:@0.371674:0.420729:0.378697:0.420729:0.381136:0.394546:0.374113:0.394546:0.000000 b:@0.382458:0.401345:0.387861:0.401345:0.387861:0.391743:0.382458:0.391743:0.000000 a:@0.378886:0.423026:0.384120:0.423026:0.384120:0.413424:0.378886:0.413424:0.000000 n:@0.264107:0.603242:0.270214:0.603242:0.270214:0.592502:0.264107:0.592502:0.000000 →:@0.270214:0.602560:0.280961:0.602560:0.280961:0.592549:0.270214:0.592549:0.000000 ∞:@0.280959:0.603167:0.289641:0.603167:0.289641:0.592408:0.280959:0.592408:0.000000 ∫:@0.186806:0.660494:0.193829:0.660494:0.196268:0.634311:0.189245:0.634311:0.000000 b:@0.197589:0.641108:0.202991:0.641108:0.202991:0.631507:0.197589:0.631507:0.000000 a:@0.194017:0.662789:0.199251:0.662789:0.199251:0.653188:0.194017:0.653188:0.000000 ∫:@0.354236:0.830200:0.361259:0.830200:0.363699:0.804016:0.356676:0.804016:0.000000 b:@0.365020:0.810814:0.370423:0.810814:0.370423:0.801212:0.365020:0.801212:0.000000 a:@0.361449:0.832495:0.366683:0.832495:0.366683:0.822893:0.361449:0.822893:0.000000 ∫:@0.293427:0.910652:0.300450:0.910652:0.302889:0.884468:0.295866:0.884468:0.000000 b:@0.304211:0.891266:0.309613:0.891266:0.309613:0.881665:0.304211:0.881665:0.000000 a:@0.300639:0.912947:0.305873:0.912947:0.305873:0.903345:0.300639:0.903345:0.000000 ∫:@0.194336:0.946292:0.201359:0.946292:0.203799:0.920108:0.196776:0.920108:0.000000 b:@0.205121:0.926906:0.210523:0.926906:0.210523:0.917305:0.205121:0.917305:0.000000 a:@0.201549:0.948587:0.206783:0.948587:0.206783:0.938986:0.201549:0.938986:0.000000 ∫:@0.295681:0.946292:0.302704:0.946292:0.305144:0.920108:0.298121:0.920108:0.000000 b:@0.306466:0.926906:0.311868:0.926906:0.311868:0.917305:0.306466:0.917305:0.000000 a:@0.302894:0.948587:0.308128:0.948587:0.308128:0.938986:0.302894:0.938986:0.000000 n:@0.263751:0.882471:0.269857:0.882471:0.269857:0.871731:0.263751:0.871731:0.000000 →:@0.269857:0.881789:0.280604:0.881789:0.280604:0.871778:0.269857:0.871778:0.000000 ∞:@0.280603:0.882396:0.289285:0.882396:0.289285:0.871636:0.280603:0.871636:0.000000 n:@0.263755:0.912100:0.269861:0.912100:0.269861:0.901359:0.263755:0.901359:0.000000 →:@0.269857:0.911420:0.280604:0.911420:0.280604:0.901409:0.269857:0.901409:0.000000 ∞:@0.280603:0.912027:0.289285:0.912027:0.289285:0.901267:0.280603:0.901267:0.000000 n:@0.266092:0.947303:0.272198:0.947303:0.272198:0.936563:0.266092:0.936563:0.000000 →:@0.272192:0.946625:0.282940:0.946625:0.282940:0.936614:0.272192:0.936614:0.000000 ∞:@0.282937:0.947231:0.291619:0.947231:0.291619:0.936472:0.282937:0.936472:0.000000 ∫:@0.680397:0.240884:0.686718:0.240884:0.688913:0.217319:0.682593:0.217319:0.000000 b:@0.690104:0.223436:0.694966:0.223436:0.694966:0.214795:0.690104:0.214795:0.000000 a:@0.686890:0.242949:0.691600:0.242949:0.691600:0.234308:0.686890:0.234308:0.000000 ∫:@0.639685:0.385016:0.646006:0.385016:0.648202:0.361451:0.641881:0.361451:0.000000 b:@0.649391:0.367569:0.654253:0.367569:0.654253:0.358928:0.649391:0.358928:0.000000 a:@0.646176:0.387082:0.650887:0.387082:0.650887:0.378441:0.646176:0.378441:0.000000 Glosario:@0.684804:0.663859:0.752269:0.663859:0.752269:0.646176:0.684804:0.646176:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 escalonada: :@0.685042:0.690673:0.766941:0.690673:0.766941:0.675412:0.685042:0.675412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 semejante :@0.766941:0.690475:0.836720:0.690475:0.836720:0.675412:0.766941:0.675412:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 en la superficie a una serie de :@0.638498:0.706317:0.831281:0.706317:0.831281:0.691254:0.638498:0.691254:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 escalones.:@0.638498:0.722159:0.703351:0.722159:0.703351:0.707096:0.638498:0.707096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a:@0.632070:0.667592:0.643474:0.666082:0.638272:0.643938:0.626867:0.645447:0.000000 c:@0.635451:0.678561:0.646050:0.677158:0.640968:0.655524:0.630369:0.656926:0.000000 b:@0.645827:0.671343:0.658540:0.669661:0.653408:0.647818:0.640695:0.649501:0.000000 ©:@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