206:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000 Integración:@0.073089:0.043661:0.176062:0.043661:0.176062:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 donde::@0.353907:0.588769:0.405355:0.588769:0.405355:0.573057:0.353907:0.573057:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.355582:0.630279:0.364491:0.630279:0.364491:0.614567:0.355582:0.614567:0.000000 ^:@0.368427:0.635975:0.386550:0.635975:0.386550:0.611901:0.368427:0.611901:0.000000 n:@0.375974:0.616124:0.382018:0.616124:0.382018:0.606301:0.375974:0.606301:0.000000 j:@0.369965:0.643191:0.372272:0.643191:0.372272:0.633368:0.369965:0.633368:0.000000 5:@0.372226:0.642837:0.381983:0.642837:0.381983:0.634109:0.372226:0.634109:0.000000 0:@0.381925:0.643191:0.387641:0.643191:0.387641:0.633192:0.381925:0.633192:0.000000 :@0.387569:0.630279:0.408257:0.630279:0.408257:0.614567:0.387569:0.614567:0.000000:0.000000:0.000000:0.000000 j:@0.391526:0.630279:0.395153:0.630279:0.395153:0.614844:0.391526:0.614844:0.000000 2:@0.395079:0.624215:0.400316:0.624215:0.400316:0.615055:0.395079:0.615055:0.000000 5:@0.434225:0.629724:0.449558:0.629724:0.449558:0.616009:0.434225:0.616009:0.000000 ( 1) ( 1) ( 1),:@0.449466:0.630279:0.723445:0.630282:0.723445:0.614569:0.449466:0.614567:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.458209:0.630279:0.467707:0.630279:0.467707:0.614844:0.458209:0.614844:0.000000 1:@0.471591:0.629724:0.486925:0.629724:0.486925:0.616009:0.471591:0.616009:0.000000 3:@0.504487:0.624215:0.509724:0.624215:0.509724:0.615055:0.504487:0.615055:0.000000 2:@0.513633:0.629724:0.528967:0.629724:0.528967:0.616009:0.513633:0.616009:0.000000 3:@0.532901:0.623833:0.541884:0.623833:0.541884:0.608120:0.532901:0.608120:0.000000 2:@0.532901:0.640225:0.541884:0.640225:0.541884:0.624513:0.532901:0.624513:0.000000 n n:@0.549026:0.630282:0.572016:0.630282:0.572016:0.614846:0.549026:0.614846:0.000000:0.000000:0.000000 1:@0.575532:0.629727:0.590865:0.629727:0.590865:0.616011:0.575532:0.616011:0.000000 2 5:@0.611629:0.629727:0.658070:0.629727:0.658070:0.616011:0.611629:0.616011:0.000000:0.000000:0.000000 n:@0.630091:0.630282:0.639589:0.630282:0.639589:0.614846:0.630091:0.614846:0.000000 n n:@0.661199:0.630282:0.684190:0.630282:0.684190:0.614846:0.661199:0.614846:0.000000:0.000000:0.000000 1:@0.687706:0.629727:0.703039:0.629727:0.703039:0.616011:0.687706:0.616011:0.000000 S:@0.355582:0.671789:0.363645:0.671789:0.363645:0.656354:0.355582:0.656354:0.000000 n:@0.363571:0.674962:0.369108:0.674962:0.369108:0.665963:0.363571:0.665963:0.000000 :@0.369070:0.671789:0.392300:0.671789:0.392300:0.656077:0.369070:0.656077:0.000000:0.000000:0.000000 5:@0.373027:0.671235:0.388360:0.671235:0.388360:0.657519:0.373027:0.657519:0.000000 ^:@0.392211:0.677485:0.410334:0.677485:0.410334:0.653411:0.392211:0.653411:0.000000 n:@0.399758:0.657634:0.405802:0.657634:0.405802:0.647811:0.399758:0.647811:0.000000 j:@0.393749:0.684701:0.396056:0.684701:0.396056:0.674878:0.393749:0.674878:0.000000 5:@0.396009:0.684348:0.405767:0.684348:0.405767:0.675619:0.396009:0.675619:0.000000 0:@0.405708:0.684701:0.411425:0.684701:0.411425:0.674702:0.405708:0.674702:0.000000 0 1 2 … ;:@0.411353:0.671789:0.624410:0.671789:0.624410:0.656077:0.411353:0.656077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.419249:0.671789:0.422876:0.671789:0.422876:0.656354:0.419249:0.656354:0.000000 2:@0.422998:0.665725:0.428235:0.665725:0.428235:0.656565:0.422998:0.656565:0.000000 5:@0.434225:0.671235:0.449558:0.671235:0.449558:0.657519:0.434225:0.657519:0.000000 2:@0.462317:0.665725:0.467554:0.665725:0.467554:0.656565:0.462317:0.656565:0.000000 1:@0.471466:0.671235:0.486799:0.671235:0.486799:0.657519:0.471466:0.657519:0.000000 2:@0.499552:0.665725:0.504789:0.665725:0.504789:0.656565:0.499552:0.656565:0.000000 1:@0.508699:0.671235:0.524032:0.671235:0.524032:0.657519:0.508699:0.657519:0.000000 2:@0.536785:0.665725:0.542022:0.665725:0.542022:0.656565:0.536785:0.656565:0.000000 1:@0.545933:0.671235:0.561266:0.671235:0.561266:0.657519:0.545933:0.657519:0.000000 1:@0.587405:0.671235:0.602738:0.671235:0.602738:0.657519:0.587405:0.657519:0.000000 n:@0.606604:0.671789:0.616102:0.671789:0.616102:0.656354:0.606604:0.656354:0.000000 2:@0.616018:0.665725:0.621255:0.665725:0.621255:0.656565:0.616018:0.656565:0.000000 5:@0.434218:0.712745:0.449551:0.712745:0.449551:0.699029:0.434218:0.699029:0.000000 :@0.449466:0.713299:0.453497:0.713299:0.453497:0.697587:0.449466:0.697587:0.000000 n n :@0.453412:0.703813:0.497110:0.703813:0.497110:0.688378:0.453412:0.688378:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.462707:0.703813:0.467585:0.703813:0.467585:0.688101:0.462707:0.688101:0.000000 1:@0.478648:0.703259:0.493981:0.703259:0.493981:0.689543:0.478648:0.689543:0.000000 1) (1:@0.495730:0.703813:0.526746:0.703813:0.526746:0.688101:0.495730:0.688101:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.526562:0.703813:0.529875:0.703813:0.529875:0.688378:0.526562:0.688378:0.000000 1 :@0.528495:0.703259:0.548246:0.703259:0.548246:0.689543:0.528495:0.689543:0.000000:0.000000 2 ):@0.548062:0.703813:0.572985:0.703813:0.572985:0.688101:0.548062:0.688101:0.000000:0.000000:0.000000 n:@0.556860:0.703813:0.568291:0.703813:0.568291:0.688378:0.556860:0.688378:0.000000:0.000000 6:@0.508707:0.720206:0.517690:0.720206:0.517690:0.704493:0.508707:0.704493:0.000000 .:@0.572893:0.713299:0.576096:0.713299:0.576096:0.697587:0.572893:0.697587:0.000000 Definición:@0.293655:0.754807:0.372946:0.754807:0.372946:0.738137:0.293655:0.738137:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 . Sea [ , ] un intervalo cerrado de, , :@0.372954:0.754807:0.691230:0.754809:0.691230:0.739097:0.372954:0.739094:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.376230:0.754807:0.380040:0.754807:0.380040:0.737860:0.376230:0.737860:0.000000 a b:@0.416739:0.754807:0.443417:0.754807:0.443417:0.739371:0.416739:0.739371:0.000000:0.000000:0.000000 R:@0.636582:0.753947:0.649872:0.753947:0.649872:0.741050:0.636582:0.741050:0.000000 n:@0.658064:0.754807:0.667562:0.754807:0.667562:0.739371:0.658064:0.739371:0.000000 [:@0.672488:0.754519:0.687124:0.754519:0.687124:0.741109:0.672488:0.741109:0.000000 Z:@0.692040:0.753949:0.704318:0.753949:0.704318:0.741052:0.692040:0.741052:0.000000 1:@0.704391:0.752993:0.719724:0.752993:0.719724:0.739277:0.704391:0.739277:0.000000 . Una partición del intervalo :@0.719798:0.754809:0.930986:0.754809:0.930986:0.739097:0.719798:0.739097:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.926898:0.754809:0.930929:0.754809:0.930929:0.739097:0.926898:0.739097:0.000000 [ , ] en subintervalos es un conjunto de puntos que se nota ( ) y se define como :@0.293652:0.773088:0.909326:0.773090:0.909326:0.757377:0.293652:0.757375:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.298456:0.773088:0.323969:0.773088:0.323969:0.757652:0.298456:0.757652:0.000000:0.000000:0.000000 n:@0.355224:0.773088:0.364722:0.773088:0.364722:0.757652:0.355224:0.757652:0.000000 t:@0.749981:0.772403:0.757783:0.772403:0.759916:0.759311:0.752115:0.759311:0.000000 n:@0.762951:0.773090:0.772450:0.773090:0.772450:0.757655:0.762951:0.757655:0.000000 t:@0.519503:0.813914:0.527304:0.813914:0.529437:0.800822:0.521636:0.800822:0.000000 ( ) { , , …, :@0.527670:0.814601:0.639445:0.814601:0.639445:0.798889:0.527670:0.798889:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.532474:0.814601:0.541972:0.814601:0.541972:0.799166:0.532474:0.799166:0.000000 5:@0.550642:0.814047:0.565975:0.814047:0.565975:0.800331:0.550642:0.800331:0.000000 x x:@0.574627:0.814601:0.601737:0.814601:0.601737:0.799166:0.574627:0.799166:0.000000:0.000000:0.000000 0:@0.582023:0.817774:0.587260:0.817774:0.587260:0.808613:0.582023:0.808613:0.000000 1:@0.601675:0.817774:0.606912:0.817774:0.606912:0.808613:0.601675:0.808613:0.000000 x:@0.639335:0.814601:0.646790:0.814601:0.646790:0.799166:0.639335:0.799166:0.000000 n:@0.646725:0.817774:0.652262:0.817774:0.652262:0.808775:0.646725:0.808775:0.000000 2:@0.652223:0.814047:0.667557:0.814047:0.667557:0.800331:0.652223:0.800331:0.000000 1:@0.667465:0.817774:0.672701:0.817774:0.672701:0.808613:0.667465:0.808613:0.000000 , },:@0.672655:0.814601:0.700623:0.814601:0.700623:0.798889:0.672655:0.798889:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.679724:0.814601:0.687179:0.814601:0.687179:0.799166:0.679724:0.799166:0.000000 n:@0.687117:0.817774:0.692654:0.817774:0.692654:0.808775:0.687117:0.808775:0.000000 donde::@0.293657:0.856109:0.345105:0.856109:0.345105:0.840396:0.293657:0.840396:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.494811:0.897616:0.502266:0.897616:0.502266:0.882181:0.494811:0.882181:0.000000 0:@0.502206:0.900794:0.507443:0.900794:0.507443:0.891633:0.502206:0.891633:0.000000 … :@0.507395:0.897621:0.620971:0.897621:0.620971:0.881909:0.507395:0.881909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 ,:@0.511353:0.897067:0.559027:0.897067:0.559027:0.883351:0.511353:0.883351:0.000000:0.000000:0.000000 a:@0.530551:0.897621:0.539810:0.897621:0.539810:0.882186:0.530551:0.882186:0.000000 x:@0.562893:0.897621:0.570348:0.897621:0.570348:0.882186:0.562893:0.882186:0.000000 1:@0.570261:0.900794:0.575498:0.900794:0.575498:0.891633:0.570261:0.891633:0.000000 ,:@0.579408:0.897067:0.594741:0.897067:0.594741:0.883351:0.579408:0.883351:0.000000 x:@0.620879:0.897621:0.628334:0.897621:0.628334:0.882186:0.620879:0.882186:0.000000 n:@0.628259:0.900794:0.633796:0.900794:0.633796:0.891795:0.628259:0.891795:0.000000 2 ,:@0.633758:0.897067:0.673479:0.897067:0.673479:0.883351:0.633758:0.883351:0.000000:0.000000:0.000000 1:@0.648997:0.900794:0.654234:0.900794:0.654234:0.891633:0.648997:0.891633:0.000000 .:@0.654188:0.897621:0.725762:0.897621:0.725762:0.881909:0.654188:0.881909:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.677344:0.897621:0.684799:0.897621:0.684799:0.882186:0.677344:0.882186:0.000000 n:@0.684719:0.900794:0.690256:0.900794:0.690256:0.891795:0.684719:0.891795:0.000000 5:@0.694175:0.897067:0.709508:0.897067:0.709508:0.883351:0.694175:0.883351:0.000000 b:@0.713374:0.897621:0.722633:0.897621:0.722633:0.882186:0.713374:0.882186:0.000000 Al conjunto ( ) se le llama subdivisión del intervalo [ , ]. Escribiremos también::@0.293670:0.939129:0.875627:0.939132:0.875627:0.923419:0.293670:0.923416:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 t:@0.381790:0.938445:0.389591:0.938445:0.391724:0.925352:0.383923:0.925352:0.000000 n:@0.394759:0.939132:0.404258:0.939132:0.404258:0.923696:0.394759:0.923696:0.000000 a b:@0.677679:0.939132:0.703191:0.939132:0.703191:0.923696:0.677679:0.923696:0.000000:0.000000:0.000000 La integral definida :@0.082576:0.188586:0.212350:0.188586:0.212350:0.174302:0.082576:0.174302:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cumple las siguientes :@0.082576:0.203715:0.228304:0.203715:0.228304:0.189431:0.082576:0.189431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 propiedades:@0.082576:0.218844:0.173203:0.218844:0.173203:0.203438:0.082576:0.203438:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ::@0.173106:0.218844:0.176018:0.218844:0.176018:0.204560:0.173106:0.204560:0.000000 • Toda integral extendida :@0.082576:0.241121:0.256246:0.241121:0.256246:0.226837:0.082576:0.226837:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a un intervalo de un :@0.096806:0.256250:0.233073:0.256250:0.233073:0.241966:0.096806:0.241966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 solo punto, [ , ], es :@0.096806:0.271379:0.230777:0.271379:0.230777:0.257095:0.096806:0.257095:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a a:@0.178886:0.271379:0.202079:0.271379:0.202079:0.257347:0.178886:0.257347:0.000000:0.000000:0.000000 igual a cero.:@0.096789:0.286508:0.175377:0.286508:0.175377:0.272224:0.096789:0.272224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Cuando la función ( ) :@0.082576:0.308784:0.244951:0.308784:0.244951:0.294500:0.082576:0.294500:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.221574:0.308784:0.236919:0.308784:0.236919:0.294752:0.221574:0.294752:0.000000:0.000000:0.000000 es mayor que cero, su :@0.096806:0.323913:0.243453:0.323913:0.243453:0.309629:0.096806:0.309629:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 integral es positiva; si :@0.096806:0.339042:0.239335:0.339042:0.239335:0.324758:0.096806:0.324758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la función es menor :@0.096806:0.354171:0.231464:0.354171:0.231464:0.339887:0.096806:0.339887:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que cero, su integral es :@0.096806:0.369300:0.251668:0.369300:0.251668:0.355016:0.096806:0.355016:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 negativa.:@0.096806:0.384429:0.156797:0.384429:0.156797:0.370145:0.096806:0.370145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Al permutar los límites :@0.082576:0.406705:0.244703:0.406705:0.244703:0.392421:0.082576:0.392421:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de una integral, esta :@0.096806:0.421834:0.229988:0.421834:0.229988:0.407550:0.096806:0.407550:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cambia de signo.:@0.096806:0.436963:0.206117:0.436963:0.206117:0.422679:0.096806:0.422679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 • Dados tres puntos tales :@0.082576:0.459239:0.254913:0.459239:0.254913:0.444955:0.082576:0.444955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 que :@0.096806:0.474368:0.126392:0.474368:0.126392:0.460084:0.096806:0.460084:0.000000:0.000000:0.000000:0.000000 a:@0.096806:0.489497:0.105223:0.489497:0.105223:0.475465:0.096806:0.475465:0.000000 , entonces se :@0.105156:0.489497:0.251807:0.489497:0.251807:0.475213:0.105156:0.475213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , ,:@0.108754:0.488993:0.152095:0.488993:0.152095:0.476524:0.108754:0.476524:0.000000:0.000000:0.000000 b:@0.126207:0.489497:0.134625:0.489497:0.134625:0.475465:0.126207:0.475465:0.000000 c:@0.155609:0.489497:0.162570:0.489497:0.162570:0.475465:0.155609:0.475465:0.000000 cumple la integración a :@0.096806:0.504626:0.255666:0.504626:0.255666:0.490342:0.096806:0.490342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 trozos::@0.096806:0.519755:0.139777:0.519755:0.139777:0.505470:0.096806:0.505470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.110245:0.544565:0.115362:0.544565:0.115362:0.526911:0.110245:0.526911:0.000000 b:@0.118042:0.535098:0.123934:0.535098:0.123934:0.525276:0.118042:0.525276:0.000000 a:@0.118042:0.547709:0.123934:0.547709:0.123934:0.537887:0.118042:0.537887:0.000000 f x dx :@0.124201:0.543261:0.161919:0.543261:0.161919:0.529229:0.124201:0.529229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.128401:0.543261:0.143914:0.543261:0.143914:0.528977:0.128401:0.528977:0.000000:0.000000:0.000000 1:@0.161869:0.542757:0.175809:0.542757:0.175809:0.530288:0.161869:0.530288:0.000000 :@0.175725:0.543261:0.179390:0.543261:0.179390:0.528977:0.175725:0.528977:0.000000 #:@0.179319:0.544651:0.184436:0.544651:0.184436:0.526996:0.179319:0.526996:0.000000 c:@0.187117:0.535184:0.191990:0.535184:0.191990:0.525361:0.187117:0.525361:0.000000 b:@0.187117:0.547795:0.193009:0.547795:0.193009:0.537973:0.187117:0.537973:0.000000 f x dx:@0.193262:0.543261:0.228035:0.543261:0.228035:0.529229:0.193262:0.529229:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) :@0.197462:0.543261:0.231700:0.543261:0.231700:0.528977:0.197462:0.528977:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.134560:0.566169:0.148499:0.566169:0.148499:0.553700:0.134560:0.553700:0.000000 :@0.148415:0.566673:0.152080:0.566673:0.152080:0.552389:0.148415:0.552389:0.000000 #:@0.152021:0.568072:0.157139:0.568072:0.157139:0.550417:0.152021:0.550417:0.000000 c:@0.159819:0.558603:0.164692:0.558603:0.164692:0.548781:0.159819:0.548781:0.000000 a:@0.159819:0.571215:0.165711:0.571215:0.165711:0.561392:0.159819:0.561392:0.000000 f x dx.:@0.165964:0.566680:0.203699:0.566680:0.203699:0.552648:0.165964:0.552648:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.170164:0.566680:0.185676:0.566680:0.185676:0.552395:0.170164:0.552395:0.000000:0.000000:0.000000 • Para todo punto del :@0.082576:0.588956:0.240634:0.588956:0.240634:0.574672:0.082576:0.574672:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.206363:0.588956:0.213140:0.588956:0.213140:0.574924:0.206363:0.574924:0.000000 intervalo [ , ] al que se :@0.096806:0.604085:0.253835:0.604085:0.253835:0.589800:0.096806:0.589800:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a b:@0.161884:0.604085:0.184826:0.604085:0.184826:0.590053:0.161884:0.590053:0.000000:0.000000:0.000000 aplican dos funciones :@0.096789:0.619214:0.242357:0.619214:0.242357:0.604929:0.096789:0.604929:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f x:@0.096789:0.634343:0.111967:0.634343:0.111967:0.620311:0.096789:0.620311:0.000000:0.000000:0.000000 ( ) y ( ), tales que :@0.100906:0.634343:0.226192:0.634343:0.226192:0.620058:0.100906:0.620058:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 g x:@0.130307:0.634343:0.149635:0.634343:0.149635:0.620311:0.130307:0.620311:0.000000:0.000000:0.000000 f x:@0.096773:0.649472:0.111950:0.649472:0.111950:0.635439:0.096773:0.635439:0.000000:0.000000:0.000000 ( ) ( ), se verifica :@0.100889:0.649472:0.233826:0.649472:0.233826:0.635187:0.100889:0.635187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.119581:0.648967:0.133520:0.648967:0.133520:0.636498:0.119581:0.636498:0.000000 g x:@0.136867:0.649472:0.156195:0.649472:0.156195:0.635439:0.136867:0.635439:0.000000:0.000000:0.000000 que::@0.096756:0.664600:0.125287:0.664600:0.125287:0.650316:0.096756:0.650316:0.000000:0.000000:0.000000:0.000000 #:@0.096806:0.689411:0.101923:0.689411:0.101923:0.671756:0.096806:0.671756:0.000000 b:@0.104603:0.679944:0.110495:0.679944:0.110495:0.670121:0.104603:0.670121:0.000000 a:@0.104603:0.692555:0.110495:0.692555:0.110495:0.682733:0.104603:0.682733:0.000000 f x dx :@0.110762:0.688508:0.148480:0.688508:0.148480:0.674476:0.110762:0.674476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ):@0.114962:0.688508:0.130475:0.688508:0.130475:0.674224:0.114962:0.674224:0.000000:0.000000:0.000000 #:@0.148430:0.688004:0.162369:0.688004:0.162369:0.675535:0.148430:0.675535:0.000000 :@0.162286:0.688508:0.165950:0.688508:0.165950:0.674224:0.162286:0.674224:0.000000 #:@0.165880:0.691047:0.170998:0.691047:0.170998:0.673393:0.165880:0.673393:0.000000 b:@0.173678:0.681580:0.179570:0.681580:0.179570:0.671758:0.173678:0.671758:0.000000 a:@0.173678:0.694191:0.179570:0.694191:0.179570:0.684369:0.173678:0.684369:0.000000 g x dx:@0.179836:0.688508:0.218759:0.688508:0.218759:0.674476:0.179836:0.674476:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) .:@0.188187:0.688508:0.221621:0.688508:0.221621:0.674224:0.188187:0.674224:0.000000:0.000000:0.000000:0.000000:0.000000 Ilustración gráfica del concepto :@0.082576:0.786445:0.231818:0.786445:0.231818:0.776446:0.082576:0.776446:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de integral definida:@0.082574:0.797035:0.173389:0.797035:0.173389:0.787036:0.082574:0.787036:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Adaptado de: :@0.193187:0.814774:0.258275:0.814774:0.258275:0.804775:0.193187:0.804775:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 http://www.hiru.eus/matematicas/la-:@0.083863:0.825364:0.255844:0.825364:0.255844:0.815365:0.083863:0.815365:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 integral-definida:@0.179329:0.835955:0.255772:0.835955:0.255772:0.825956:0.179329:0.825956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Competencia :@0.078581:0.145303:0.187141:0.145303:0.187141:0.128356:0.078581:0.128356:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.078581:0.161945:0.176057:0.161945:0.176057:0.144998:0.078581:0.144998:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 donde::@0.323781:0.136836:0.375229:0.136836:0.375229:0.121124:0.323781:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 :@0.511264:0.181206:0.528162:0.181206:0.528162:0.165493:0.511264:0.165493:0.000000:0.000000:0.000000 j n n :@0.528070:0.181206:0.651126:0.181206:0.651126:0.165770:0.528070:0.165770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 1:@0.534880:0.180651:0.582868:0.180651:0.582868:0.166935:0.534880:0.166935:0.000000:0.000000:0.000000 (:@0.551797:0.181206:0.556675:0.181206:0.556675:0.165493:0.551797:0.165493:0.000000 1):@0.584451:0.181206:0.598054:0.181206:0.598054:0.165493:0.584451:0.165493:0.000000:0.000000 2:@0.597778:0.175142:0.603015:0.175142:0.603015:0.165981:0.597778:0.165981:0.000000 2 2 5:@0.604721:0.180651:0.677485:0.180651:0.677485:0.166935:0.604721:0.166935:0.000000:0.000000:0.000000:0.000000:0.000000 1 (:@0.649671:0.181206:0.695101:0.181206:0.695101:0.165493:0.649671:0.165493:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n n :@0.680982:0.181206:0.724331:0.181206:0.724331:0.165770:0.680982:0.165770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.705961:0.180651:0.721294:0.180651:0.721294:0.166935:0.705961:0.166935:0.000000 1),:@0.722877:0.181206:0.739425:0.181206:0.739425:0.165493:0.722877:0.165493:0.000000:0.000000:0.000000 S:@0.486013:0.225570:0.494075:0.225570:0.494075:0.210135:0.486013:0.210135:0.000000 n:@0.494031:0.228747:0.499569:0.228747:0.499569:0.219749:0.494031:0.219749:0.000000 :@0.499530:0.225575:0.520735:0.225575:0.520735:0.209862:0.499530:0.209862:0.000000:0.000000:0.000000 5:@0.501647:0.225020:0.516980:0.225020:0.516980:0.211305:0.501647:0.211305:0.000000 ^:@0.520647:0.231271:0.538769:0.231271:0.538769:0.207197:0.520647:0.207197:0.000000 n:@0.528194:0.211419:0.534238:0.211419:0.534238:0.201597:0.528194:0.201597:0.000000 j:@0.522185:0.238495:0.524492:0.238495:0.524492:0.228673:0.522185:0.228673:0.000000 5:@0.524445:0.238142:0.534203:0.238142:0.534203:0.229414:0.524445:0.229414:0.000000 0:@0.534144:0.238495:0.539860:0.238495:0.539860:0.228496:0.534144:0.228496:0.000000 0:@0.539789:0.225575:0.578701:0.225575:0.578701:0.209862:0.539789:0.209862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.543746:0.225575:0.547372:0.225575:0.547372:0.210140:0.543746:0.210140:0.000000 5 1 1 1:@0.550888:0.225020:0.650619:0.225020:0.650619:0.211305:0.550888:0.211305:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.578425:0.225575:0.653656:0.225575:0.653656:0.210140:0.578425:0.210140:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.597201:0.225575:0.606183:0.225575:0.606183:0.209862:0.597201:0.209862:0.000000 2:@0.624701:0.225575:0.633684:0.225575:0.633684:0.209862:0.624701:0.209862:0.000000 … :@0.652202:0.225575:0.706209:0.225575:0.706209:0.209862:0.652202:0.209862:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.674106:0.225575:0.683604:0.225575:0.683604:0.210140:0.674106:0.210140:0.000000 5:@0.687120:0.225020:0.702453:0.225020:0.702453:0.211305:0.687120:0.211305:0.000000 n n :@0.706312:0.217351:0.750011:0.217351:0.750011:0.201916:0.706312:0.201916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.715608:0.217351:0.720486:0.217351:0.720486:0.201639:0.715608:0.201639:0.000000 1:@0.731549:0.216796:0.746882:0.216796:0.746882:0.203081:0.731549:0.203081:0.000000 1:@0.748631:0.217351:0.757613:0.217351:0.757613:0.201639:0.748631:0.201639:0.000000 2:@0.727481:0.233743:0.736463:0.233743:0.736463:0.218031:0.727481:0.218031:0.000000 . :@0.757705:0.225575:0.772744:0.225575:0.772744:0.209862:0.757705:0.209862:0.000000:0.000000:0.000000:0.000000 3. Calculemos la suma de los cuadrados de los primeros números naturales: :@0.293660:0.269944:0.870925:0.269944:0.870925:0.254232:0.293660:0.254232:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.646025:0.269944:0.655523:0.269944:0.655523:0.254509:0.646025:0.254509:0.000000 S:@0.493944:0.314309:0.502007:0.314309:0.502007:0.298873:0.493944:0.298873:0.000000 n:@0.501943:0.317486:0.507481:0.317486:0.507481:0.308487:0.501943:0.308487:0.000000 :@0.507442:0.314314:0.530672:0.314314:0.530672:0.298601:0.507442:0.298601:0.000000:0.000000:0.000000 5:@0.511400:0.313759:0.526733:0.313759:0.526733:0.300043:0.511400:0.300043:0.000000 ^:@0.530583:0.320010:0.548706:0.320010:0.548706:0.295936:0.530583:0.295936:0.000000 n:@0.538130:0.300157:0.544174:0.300157:0.544174:0.290334:0.538130:0.290334:0.000000 j:@0.532121:0.327233:0.534429:0.327233:0.534429:0.317410:0.532121:0.317410:0.000000 5:@0.534382:0.326880:0.544139:0.326880:0.544139:0.318152:0.534382:0.318152:0.000000 0:@0.544081:0.327233:0.549797:0.327233:0.549797:0.317234:0.544081:0.317234:0.000000 0 1 2 … .:@0.549725:0.314314:0.756745:0.314314:0.756745:0.298601:0.549725:0.298601:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.553683:0.314314:0.557309:0.314314:0.557309:0.298879:0.553683:0.298879:0.000000 2:@0.557419:0.308250:0.562656:0.308250:0.562656:0.299089:0.557419:0.299089:0.000000 5:@0.566566:0.313759:0.581899:0.313759:0.581899:0.300043:0.566566:0.300043:0.000000 2:@0.594654:0.308250:0.599891:0.308250:0.599891:0.299089:0.594654:0.299089:0.000000 1:@0.603801:0.313759:0.619134:0.313759:0.619134:0.300043:0.603801:0.300043:0.000000 2:@0.631887:0.308250:0.637124:0.308250:0.637124:0.299089:0.631887:0.299089:0.000000 1:@0.641035:0.313759:0.656368:0.313759:0.656368:0.300043:0.641035:0.300043:0.000000 2:@0.669121:0.308250:0.674358:0.308250:0.674358:0.299089:0.669121:0.299089:0.000000 1:@0.678268:0.313759:0.693601:0.313759:0.693601:0.300043:0.678268:0.300043:0.000000 1:@0.719740:0.313759:0.735073:0.313759:0.735073:0.300043:0.719740:0.300043:0.000000 n:@0.738938:0.314314:0.748436:0.314314:0.748436:0.298879:0.738938:0.298879:0.000000 2:@0.748353:0.308250:0.753590:0.308250:0.753590:0.299089:0.748353:0.299089:0.000000 Para se tiene ( 1) 3 3 1 3 3 1.:@0.323788:0.358678:0.828068:0.358683:0.828068:0.342971:0.323788:0.342966:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.358246:0.358678:0.361872:0.358678:0.361872:0.343243:0.358246:0.343243:0.000000 [:@0.365383:0.358393:0.380019:0.358393:0.380019:0.344983:0.365383:0.344983:0.000000 N:@0.383529:0.357823:0.397850:0.357823:0.397850:0.344926:0.383529:0.344926:0.000000 j:@0.466712:0.358683:0.470338:0.358683:0.470338:0.343248:0.466712:0.343248:0.000000 1:@0.474222:0.358128:0.489555:0.358128:0.489555:0.344413:0.474222:0.344413:0.000000 3:@0.507101:0.352619:0.512337:0.352619:0.512337:0.343459:0.507101:0.343459:0.000000 2 5 1:@0.516247:0.358128:0.595365:0.358128:0.595365:0.344413:0.516247:0.344413:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.535446:0.358683:0.539072:0.358683:0.539072:0.343248:0.535446:0.343248:0.000000 3:@0.538992:0.352619:0.544229:0.352619:0.544229:0.343459:0.538992:0.343459:0.000000 j:@0.567337:0.358683:0.570964:0.358683:0.570964:0.343248:0.567337:0.343248:0.000000 3:@0.570883:0.352619:0.576120:0.352619:0.576120:0.343459:0.570883:0.343459:0.000000 j:@0.608121:0.358683:0.611748:0.358683:0.611748:0.343248:0.608121:0.343248:0.000000 2:@0.611677:0.352619:0.616914:0.352619:0.616914:0.343459:0.611677:0.343459:0.000000 1:@0.620824:0.358128:0.636157:0.358128:0.636157:0.344413:0.620824:0.344413:0.000000 j:@0.648913:0.358683:0.652540:0.358683:0.652540:0.343248:0.648913:0.343248:0.000000 1 2 5:@0.656424:0.358128:0.735697:0.358128:0.735697:0.344413:0.656424:0.344413:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.707669:0.358683:0.711296:0.358683:0.711296:0.343248:0.707669:0.343248:0.000000 3:@0.711217:0.352619:0.716454:0.352619:0.716454:0.343459:0.711217:0.343459:0.000000 j:@0.748453:0.358683:0.752079:0.358683:0.752079:0.343248:0.748453:0.343248:0.000000 2:@0.752011:0.352619:0.757248:0.352619:0.757248:0.343459:0.752011:0.343459:0.000000 1:@0.761158:0.358128:0.776491:0.358128:0.776491:0.344413:0.761158:0.344413:0.000000 j:@0.789247:0.358683:0.792873:0.358683:0.792873:0.343248:0.789247:0.343248:0.000000 1:@0.796757:0.358128:0.812090:0.358128:0.812090:0.344413:0.796757:0.344413:0.000000 Por la propiedad iii), resulta que:@0.323783:0.403048:0.551276:0.403048:0.551276:0.387335:0.323783:0.387335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ^:@0.323781:0.453117:0.341904:0.453117:0.341904:0.429043:0.323781:0.429043:0.000000 n:@0.331328:0.433265:0.337372:0.433265:0.337372:0.423443:0.331328:0.423443:0.000000 j:@0.325319:0.460341:0.327627:0.460341:0.327627:0.450518:0.325319:0.450518:0.000000 5:@0.327580:0.459988:0.337337:0.459988:0.337337:0.451260:0.327580:0.451260:0.000000 0:@0.337279:0.460341:0.342995:0.460341:0.342995:0.450342:0.337279:0.450342:0.000000 [( 1) ] ( 1) , y por las propiedades i) y ii), resulta que:@0.342923:0.447421:0.814358:0.447421:0.814358:0.431708:0.342923:0.431708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.361514:0.447421:0.365141:0.447421:0.365141:0.431985:0.361514:0.431985:0.000000 1:@0.369024:0.446866:0.384358:0.446866:0.384358:0.433150:0.369024:0.433150:0.000000 3:@0.401923:0.441357:0.407160:0.441357:0.407160:0.432196:0.401923:0.432196:0.000000 2:@0.411072:0.446866:0.426405:0.446866:0.426405:0.433150:0.411072:0.433150:0.000000 j:@0.430270:0.447421:0.433897:0.447421:0.433897:0.431985:0.430270:0.431985:0.000000 3:@0.433815:0.441357:0.439051:0.441357:0.439051:0.432196:0.433815:0.432196:0.000000 5:@0.447749:0.446866:0.463082:0.446866:0.463082:0.433150:0.447749:0.433150:0.000000 n:@0.471734:0.447421:0.481232:0.447421:0.481232:0.431985:0.471734:0.431985:0.000000 1:@0.485116:0.446866:0.500449:0.446866:0.500449:0.433150:0.485116:0.433150:0.000000 3:@0.518014:0.441357:0.523251:0.441357:0.523251:0.432196:0.518014:0.432196:0.000000 ( 1) :@0.353895:0.491790:0.433393:0.491790:0.433393:0.476077:0.353895:0.476077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.358700:0.491790:0.368198:0.491790:0.368198:0.476355:0.358700:0.476355:0.000000 1:@0.372082:0.491235:0.387415:0.491235:0.387415:0.477520:0.372082:0.477520:0.000000 3:@0.404972:0.485726:0.410209:0.485726:0.410209:0.476566:0.404972:0.476566:0.000000 5:@0.414121:0.491235:0.429454:0.491235:0.429454:0.477520:0.414121:0.477520:0.000000 ^:@0.433304:0.497486:0.451427:0.497486:0.451427:0.473412:0.433304:0.473412:0.000000 n:@0.440851:0.477635:0.446895:0.477635:0.446895:0.467812:0.440851:0.467812:0.000000 j:@0.434842:0.504710:0.437150:0.504710:0.437150:0.494888:0.434842:0.494888:0.000000 5:@0.437103:0.504357:0.446860:0.504357:0.446860:0.495629:0.437103:0.495629:0.000000 0:@0.446802:0.504710:0.452518:0.504710:0.452518:0.494711:0.446802:0.494711:0.000000 [( 1) ] :@0.452446:0.491790:0.575440:0.491790:0.575440:0.476077:0.452446:0.476077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.469933:0.491790:0.473559:0.491790:0.473559:0.476355:0.469933:0.476355:0.000000 1:@0.477443:0.491235:0.492776:0.491235:0.492776:0.477520:0.477443:0.477520:0.000000 3:@0.510342:0.485726:0.515579:0.485726:0.515579:0.476566:0.510342:0.476566:0.000000 2:@0.519489:0.491235:0.534822:0.491235:0.534822:0.477520:0.519489:0.477520:0.000000 j:@0.538687:0.491790:0.542314:0.491790:0.542314:0.476355:0.538687:0.476355:0.000000 3:@0.542233:0.485726:0.547470:0.485726:0.547470:0.476566:0.542233:0.476566:0.000000 5:@0.556168:0.491235:0.571501:0.491235:0.571501:0.477520:0.556168:0.477520:0.000000 ^:@0.575363:0.497486:0.593486:0.497486:0.593486:0.473412:0.575363:0.473412:0.000000 n:@0.582910:0.477635:0.588954:0.477635:0.588954:0.467812:0.582910:0.467812:0.000000 j:@0.576901:0.504710:0.579209:0.504710:0.579209:0.494888:0.576901:0.494888:0.000000 5:@0.579162:0.504357:0.588919:0.504357:0.588919:0.495629:0.579162:0.495629:0.000000 0:@0.588861:0.504710:0.594577:0.504710:0.594577:0.494711:0.588861:0.494711:0.000000 (3 3 1):@0.594505:0.491790:0.693447:0.491790:0.693447:0.476077:0.594505:0.476077:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.612157:0.491790:0.615784:0.491790:0.615784:0.476355:0.612157:0.476355:0.000000 2:@0.615713:0.485726:0.620950:0.485726:0.620950:0.476566:0.615713:0.476566:0.000000 1:@0.624862:0.491235:0.640195:0.491235:0.640195:0.477520:0.624862:0.477520:0.000000 j:@0.652951:0.491790:0.656578:0.491790:0.656578:0.476355:0.652951:0.476355:0.000000 1:@0.660461:0.491235:0.675795:0.491235:0.675795:0.477520:0.660461:0.477520:0.000000 5:@0.353895:0.535605:0.369229:0.535605:0.369229:0.521889:0.353895:0.521889:0.000000 3 :@0.369143:0.536160:0.386041:0.536160:0.386041:0.520447:0.369143:0.520447:0.000000:0.000000:0.000000 ^:@0.385946:0.541856:0.404069:0.541856:0.404069:0.517782:0.385946:0.517782:0.000000 n:@0.393493:0.522004:0.399537:0.522004:0.399537:0.512181:0.393493:0.512181:0.000000 j:@0.387484:0.549080:0.389791:0.549080:0.389791:0.539257:0.387484:0.539257:0.000000 5:@0.389744:0.548727:0.399502:0.548727:0.399502:0.539999:0.389744:0.539999:0.000000 0:@0.399443:0.549080:0.405160:0.549080:0.405160:0.539081:0.399443:0.539081:0.000000 3 :@0.405088:0.536160:0.455724:0.536160:0.455724:0.520447:0.405088:0.520447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.410886:0.536160:0.414512:0.536160:0.414512:0.520724:0.410886:0.520724:0.000000 2:@0.414438:0.530096:0.419675:0.530096:0.419675:0.520935:0.414438:0.520935:0.000000 1:@0.423585:0.535605:0.438918:0.535605:0.438918:0.521889:0.423585:0.521889:0.000000 ^:@0.455622:0.541856:0.473745:0.541856:0.473745:0.517782:0.455622:0.517782:0.000000 n:@0.463169:0.522004:0.469213:0.522004:0.469213:0.512181:0.463169:0.512181:0.000000 j:@0.457160:0.549080:0.459468:0.549080:0.459468:0.539257:0.457160:0.539257:0.000000 5:@0.459421:0.548727:0.469178:0.548727:0.469178:0.539999:0.459421:0.539999:0.000000 0:@0.469120:0.549080:0.474836:0.549080:0.474836:0.539081:0.469120:0.539081:0.000000 :@0.474764:0.536160:0.505136:0.536160:0.505136:0.520447:0.474764:0.520447:0.000000:0.000000:0.000000:0.000000:0.000000 j:@0.478353:0.536160:0.481980:0.536160:0.481980:0.520724:0.478353:0.520724:0.000000 1:@0.485864:0.535605:0.501197:0.535605:0.501197:0.521889:0.485864:0.521889:0.000000 ^:@0.505049:0.541856:0.523172:0.541856:0.523172:0.517782:0.505049:0.517782:0.000000 n:@0.512594:0.522004:0.518639:0.522004:0.518639:0.512181:0.512594:0.512181:0.000000 j:@0.506585:0.549080:0.508893:0.549080:0.508893:0.539257:0.506585:0.539257:0.000000 5:@0.508846:0.548727:0.518603:0.548727:0.518603:0.539999:0.508846:0.539999:0.000000 0:@0.518545:0.549080:0.524261:0.549080:0.524261:0.539081:0.518545:0.539081:0.000000 1 3:@0.524189:0.536160:0.569177:0.536160:0.569177:0.520447:0.524189:0.520447:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.540995:0.535605:0.556328:0.535605:0.556328:0.521889:0.540995:0.521889:0.000000 ^:@0.569086:0.541856:0.587209:0.541856:0.587209:0.517782:0.569086:0.517782:0.000000 n:@0.576633:0.522004:0.582677:0.522004:0.582677:0.512181:0.576633:0.512181:0.000000 j:@0.570624:0.549080:0.572932:0.549080:0.572932:0.539257:0.570624:0.539257:0.000000 5:@0.572885:0.548727:0.582642:0.548727:0.582642:0.539999:0.572885:0.539999:0.000000 0:@0.582584:0.549080:0.588300:0.549080:0.588300:0.539081:0.582584:0.539081:0.000000 :@0.588228:0.536160:0.606799:0.536160:0.606799:0.520447:0.588228:0.520447:0.000000:0.000000:0.000000 j:@0.594026:0.536160:0.597653:0.536160:0.597653:0.520724:0.594026:0.520724:0.000000 2:@0.597579:0.530096:0.602816:0.530096:0.602816:0.520935:0.597579:0.520935:0.000000 1 :@0.606726:0.535605:0.626569:0.535605:0.626569:0.521889:0.606726:0.521889:0.000000:0.000000 3:@0.626552:0.529715:0.635535:0.529715:0.635535:0.514002:0.626552:0.514002:0.000000 2:@0.626552:0.546107:0.635535:0.546107:0.635535:0.530394:0.626552:0.530394:0.000000 ( 1) ,:@0.635516:0.536163:0.732430:0.536163:0.732430:0.520451:0.635516:0.520451:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n n:@0.639106:0.536163:0.662096:0.536163:0.662096:0.520728:0.639106:0.520728:0.000000:0.000000:0.000000 1:@0.665612:0.535609:0.680945:0.535609:0.680945:0.521893:0.665612:0.521893:0.000000 1:@0.701709:0.535609:0.717042:0.535609:0.717042:0.521893:0.701709:0.521893:0.000000 n:@0.720171:0.536163:0.729669:0.536163:0.729669:0.520728:0.720171:0.520728:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000