220:@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 5 :@0.323781:0.143564:0.356764:0.143562:0.356764:0.129847:0.323781:0.129848:0.000000:0.000000:0.000000 :@0.339022:0.144118:0.343053:0.144118:0.343053:0.128406:0.339022:0.128406:0.000000 1:@0.343124:0.136836:0.352107:0.136836:0.352107:0.121124:0.343124:0.121124:0.000000 2:@0.343124:0.153228:0.352107:0.153228:0.352107:0.137516:0.343124:0.137516:0.000000 a d:@0.356671:0.144117:0.379920:0.144117:0.379920:0.128682:0.356671:0.128682:0.000000:0.000000:0.000000 ( ) ( ).:@0.365857:0.144117:0.510834:0.144118:0.510834:0.128406:0.365857:0.128404:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.379858:0.138054:0.385095:0.138054:0.385095:0.128894:0.379858:0.128894:0.000000 2:@0.389005:0.143564:0.404338:0.143564:0.404338:0.129848:0.389005:0.129848:0.000000 c:@0.408203:0.144118:0.415861:0.144118:0.415861:0.128683:0.408203:0.128683:0.000000 2:@0.415781:0.138054:0.421017:0.138054:0.421017:0.128894:0.415781:0.128894:0.000000 1:@0.429713:0.143564:0.445046:0.143564:0.445046:0.129848:0.429713:0.129848:0.000000 b d:@0.448912:0.144118:0.472160:0.144118:0.472160:0.128683:0.448912:0.128683:0.000000:0.000000:0.000000 2:@0.476044:0.143564:0.491377:0.143564:0.491377:0.129848:0.476044:0.129848:0.000000 c:@0.495243:0.144118:0.502900:0.144118:0.502900:0.128683:0.495243:0.128683:0.000000 Este resultado se obtiene de modo similar a los tratados en la:@0.323779:0.183837:0.766222:0.183837:0.766222:0.168124:0.323779:0.168124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 sección precedente, esto es, sea :@0.323779:0.223555:0.590844:0.223565:0.590844:0.207853:0.323779:0.207843:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 n:@0.558877:0.223555:0.568375:0.223555:0.568375:0.208120:0.558877:0.208120:0.000000 [:@0.572264:0.223275:0.586900:0.223275:0.586900:0.209866:0.572264:0.209866:0.000000 Z:@0.590770:0.222706:0.603048:0.222706:0.603048:0.209808:0.590770:0.209808:0.000000 1:@0.602956:0.221749:0.618289:0.221749:0.618289:0.208033:0.602956:0.208033:0.000000 , :@0.618197:0.223565:0.657920:0.223565:0.657920:0.207853:0.618197:0.207853:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 h:@0.625265:0.223565:0.634763:0.223565:0.634763:0.208130:0.625265:0.208130:0.000000 5:@0.638647:0.223011:0.653980:0.223011:0.653980:0.209295:0.638647:0.209295:0.000000 d c:@0.658047:0.216235:0.693794:0.216235:0.693794:0.200800:0.658047:0.200800:0.000000:0.000000:0.000000:0.000000:0.000000 2:@0.669054:0.215681:0.684388:0.215681:0.684388:0.201965:0.669054:0.201965:0.000000 n:@0.671171:0.232628:0.680669:0.232628:0.680669:0.217192:0.671171:0.217192:0.000000 , , 0, 1, … n.:@0.693738:0.223572:0.878224:0.223565:0.878224:0.207853:0.693738:0.207859:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.700807:0.223572:0.708262:0.223572:0.708262:0.208136:0.700807:0.208136:0.000000 j:@0.708202:0.226738:0.710316:0.226738:0.710316:0.217739:0.708202:0.217739:0.000000 5 1:@0.714234:0.223011:0.760307:0.223011:0.760307:0.209295:0.714234:0.209295:0.000000:0.000000:0.000000 c:@0.733433:0.223565:0.741090:0.223565:0.741090:0.208130:0.733433:0.208130:0.000000 jh j:@0.764173:0.223565:0.787863:0.223565:0.787863:0.208130:0.764173:0.208130:0.000000:0.000000:0.000000:0.000000 5:@0.791747:0.223011:0.807080:0.223011:0.807080:0.209295:0.791747:0.209295:0.000000 Se define la sucesión de funciones escalonadas ( ) como sigue::@0.323798:0.263284:0.786051:0.263289:0.786051:0.247576:0.323798:0.247571:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 p:@0.673812:0.263284:0.683071:0.263284:0.683071:0.247849:0.673812:0.247849:0.000000 n:@0.682994:0.266461:0.688531:0.266461:0.688531:0.257463:0.682994:0.257463:0.000000 p x:@0.323771:0.303007:0.350731:0.303012:0.350731:0.287577:0.323771:0.287572:0.000000:0.000000:0.000000 n:@0.332973:0.306185:0.338510:0.306185:0.338510:0.297186:0.332973:0.297186:0.000000 ( ) (:@0.338472:0.303012:0.388098:0.303012:0.388098:0.287300:0.338472:0.287300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.359401:0.302458:0.374734:0.302458:0.374734:0.288742:0.359401:0.288742:0.000000 f x:@0.378600:0.303012:0.395479:0.303012:0.395479:0.287577:0.378600:0.287577:0.000000:0.000000:0.000000 j:@0.395410:0.306185:0.397525:0.306185:0.397525:0.297186:0.395410:0.297186:0.000000 2 5:@0.397485:0.302458:0.441992:0.302458:0.441992:0.288742:0.397485:0.288742:0.000000:0.000000:0.000000 1:@0.412727:0.306185:0.417963:0.306185:0.417963:0.297024:0.412727:0.297024:0.000000 ) :@0.417916:0.303012:0.445932:0.303012:0.445932:0.287300:0.417916:0.287300:0.000000:0.000000:0.000000:0.000000 ax:@0.445858:0.303012:0.462498:0.303012:0.462498:0.287577:0.445858:0.287577:0.000000:0.000000 j:@0.462436:0.306185:0.464550:0.306185:0.464550:0.297186:0.462436:0.297186:0.000000 2 1:@0.464513:0.302458:0.504234:0.302458:0.504234:0.288742:0.464513:0.288742:0.000000:0.000000:0.000000 1:@0.479754:0.306185:0.484991:0.306185:0.484991:0.297024:0.479754:0.297024:0.000000 , 1, …, .:@0.484943:0.303012:0.616905:0.303012:0.616905:0.287300:0.484943:0.287300:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b:@0.508100:0.303012:0.517358:0.303012:0.517358:0.287577:0.508100:0.287577:0.000000 j:@0.536207:0.303012:0.539834:0.303012:0.539834:0.287577:0.536207:0.287577:0.000000 5:@0.543718:0.302458:0.559051:0.302458:0.559051:0.288742:0.543718:0.288742:0.000000 n:@0.604278:0.303012:0.613776:0.303012:0.613776:0.287577:0.604278:0.287577:0.000000 Entonces,:@0.323769:0.342731:0.393849:0.342731:0.393849:0.327018:0.323769:0.327018:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.455052:0.385304:0.461564:0.385304:0.461564:0.362835:0.455052:0.362835:0.000000 d:@0.463139:0.370670:0.469031:0.370670:0.469031:0.360848:0.463139:0.360848:0.000000 c:@0.463139:0.388321:0.468012:0.388321:0.468012:0.378498:0.463139:0.378498:0.000000 f( ) lím:@0.472925:0.382458:0.558040:0.380212:0.558040:0.364499:0.472925:0.366746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x dx:@0.482460:0.382458:0.511286:0.382458:0.511286:0.367023:0.482460:0.367023:0.000000:0.000000:0.000000:0.000000 5:@0.515188:0.381904:0.530521:0.381904:0.530521:0.368188:0.515188:0.368188:0.000000 n:@0.534373:0.384729:0.540418:0.384729:0.540418:0.374906:0.534373:0.374906:0.000000 →:@0.540371:0.384464:0.551932:0.384464:0.551932:0.373653:0.540371:0.373653:0.000000 `:@0.551874:0.384376:0.559687:0.384376:0.559687:0.375648:0.551874:0.375648:0.000000 #:@0.559608:0.385304:0.566121:0.385304:0.566121:0.362835:0.559608:0.362835:0.000000 d:@0.567696:0.370670:0.573588:0.370670:0.573588:0.360848:0.567696:0.360848:0.000000 c:@0.567696:0.388321:0.572569:0.388321:0.572569:0.378498:0.567696:0.378498:0.000000 p x:@0.577482:0.382458:0.604431:0.382458:0.604431:0.367023:0.577482:0.367023:0.000000:0.000000:0.000000 n:@0.586673:0.385631:0.592211:0.385631:0.592211:0.376632:0.586673:0.376632:0.000000 ( ) ( ) ( ).:@0.592172:0.382458:0.795651:0.382458:0.795651:0.366746:0.592172:0.366746:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.613101:0.381904:0.628435:0.381904:0.628435:0.368188:0.613101:0.368188:0.000000 1:@0.632449:0.375176:0.641432:0.375176:0.641432:0.359464:0.632449:0.359464:0.000000 2:@0.632449:0.391568:0.641432:0.391568:0.641432:0.375856:0.632449:0.375856:0.000000 a d:@0.641487:0.382457:0.664735:0.382457:0.664735:0.367022:0.641487:0.367022:0.000000:0.000000:0.000000 2:@0.664673:0.376395:0.669910:0.376395:0.669910:0.367234:0.664673:0.367234:0.000000 2:@0.673822:0.381904:0.689155:0.381904:0.689155:0.368188:0.673822:0.368188:0.000000 c:@0.693021:0.382458:0.700678:0.382458:0.700678:0.367023:0.693021:0.367023:0.000000 2:@0.700596:0.376395:0.705833:0.376395:0.705833:0.367234:0.700596:0.367234:0.000000 1:@0.714530:0.381904:0.729864:0.381904:0.729864:0.368188:0.714530:0.368188:0.000000 b d:@0.733729:0.382458:0.756977:0.382458:0.756977:0.367023:0.733729:0.367023:0.000000:0.000000:0.000000 2:@0.760861:0.381904:0.776195:0.381904:0.776195:0.368188:0.760861:0.368188:0.000000 c:@0.780060:0.382458:0.787718:0.382458:0.787718:0.367023:0.780060:0.367023:0.000000 2. Cálculo del área de una región limitada superiormente por una porción de :@0.293660:0.422182:0.930592:0.422182:0.930592:0.405512:0.293660:0.405512:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 parábola. :@0.323784:0.440460:0.398846:0.440460:0.398846:0.423791:0.323784:0.423791:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Sea la función definida por: :@0.323784:0.480179:0.533454:0.480179:0.533454:0.464466:0.323784:0.464466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 f:@0.353402:0.480179:0.358096:0.480179:0.358096:0.464743:0.353402:0.464743:0.000000 f x:@0.323766:0.519897:0.340645:0.519897:0.340645:0.504462:0.323766:0.504462:0.000000:0.000000:0.000000 ( ) ( 1) 1, , es un polinomio de grado 2.:@0.328386:0.519897:0.734081:0.519910:0.734081:0.504197:0.328386:0.504185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.349315:0.519342:0.364649:0.519342:0.364649:0.505627:0.349315:0.505627:0.000000 1:@0.368685:0.512628:0.377667:0.512628:0.377667:0.496915:0.368685:0.496915:0.000000 4:@0.368685:0.529020:0.377667:0.529020:0.377667:0.513307:0.368685:0.513307:0.000000 x:@0.382527:0.519909:0.389982:0.519909:0.389982:0.504473:0.382527:0.504473:0.000000 2:@0.393866:0.519354:0.409199:0.519354:0.409199:0.505638:0.393866:0.505638:0.000000 2:@0.426755:0.513846:0.431991:0.513846:0.431991:0.504685:0.426755:0.504685:0.000000 1:@0.435901:0.519355:0.451235:0.519355:0.451235:0.505639:0.435901:0.505639:0.000000 x:@0.471059:0.519910:0.478514:0.519910:0.478514:0.504475:0.471059:0.504475:0.000000 [:@0.482400:0.519620:0.497036:0.519620:0.497036:0.506210:0.482400:0.506210:0.000000 R:@0.500906:0.519050:0.514196:0.519050:0.514196:0.506153:0.500906:0.506153:0.000000 f:@0.521172:0.519910:0.525866:0.519910:0.525866:0.504475:0.521172:0.504475:0.000000 Consideremos la región como el conjunto definido por :@0.323773:0.559628:0.738442:0.559628:0.738442:0.543916:0.323773:0.543916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.499378:0.559628:0.507440:0.559628:0.507440:0.544193:0.499378:0.544193:0.000000 S:@0.323754:0.599347:0.331817:0.599347:0.331817:0.583912:0.323754:0.583912:0.000000 {( , ) :@0.331651:0.599347:0.412604:0.599357:0.412604:0.583644:0.331651:0.583634:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.335517:0.598792:0.350850:0.598792:0.350850:0.585076:0.335517:0.585076:0.000000 x y:@0.363937:0.599347:0.385584:0.599347:0.385584:0.583912:0.363937:0.583912:0.000000:0.000000:0.000000 [:@0.394025:0.599067:0.408661:0.599067:0.408661:0.585657:0.394025:0.585657:0.000000 R:@0.412531:0.598497:0.425821:0.598497:0.425821:0.585600:0.412531:0.585600:0.000000 2 :@0.425720:0.593293:0.433211:0.593293:0.433211:0.584133:0.425720:0.584133:0.000000:0.000000 | 0 ( ), 2 3}. Ver Figura 2.3.:@0.433107:0.599357:0.739022:0.599357:0.739022:0.583644:0.433107:0.583644:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 # #:@0.457220:0.598802:0.502741:0.598802:0.502741:0.585087:0.457220:0.585087:0.000000:0.000000:0.000000 y:@0.476235:0.599357:0.483708:0.599357:0.483708:0.583922:0.476235:0.583922:0.000000 f x:@0.506423:0.599357:0.523118:0.599357:0.523118:0.583922:0.506423:0.583922:0.000000:0.000000:0.000000 2 # #:@0.542262:0.598802:0.615578:0.598802:0.615578:0.585087:0.542262:0.585087:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.589090:0.599357:0.596545:0.599357:0.596545:0.583922:0.589090:0.583922:0.000000 Calculemos el área de la región . En primer lugar, una primitiva de la función está :@0.323786:0.639075:0.930968:0.639075:0.930968:0.623363:0.323786:0.623363:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 S:@0.550195:0.639075:0.558258:0.639075:0.558258:0.623640:0.550195:0.623640:0.000000 P:@0.780047:0.639075:0.788809:0.639075:0.788809:0.623640:0.780047:0.623640:0.000000 f:@0.889220:0.639075:0.893914:0.639075:0.893914:0.623640:0.889220:0.623640:0.000000 definida por: :@0.323805:0.657354:0.419588:0.657354:0.419588:0.641641:0.323805:0.641641:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P x:@0.323805:0.697072:0.344752:0.697072:0.344752:0.681637:0.323805:0.681637:0.000000:0.000000:0.000000 ( ) :@0.332493:0.697072:0.353514:0.697072:0.353514:0.681360:0.332493:0.681360:0.000000:0.000000:0.000000:0.000000 5 :@0.353422:0.696517:0.373265:0.696517:0.373265:0.682802:0.353422:0.682802:0.000000:0.000000 #:@0.373161:0.699139:0.380139:0.699139:0.380139:0.675065:0.373161:0.675065:0.000000 1:@0.380305:0.702623:0.385699:0.702623:0.385699:0.671890:0.380305:0.671890:0.000000 1:@0.386699:0.689802:0.395681:0.689802:0.395681:0.674089:0.386699:0.674089:0.000000 4:@0.386699:0.706194:0.395681:0.706194:0.395681:0.690481:0.386699:0.690481:0.000000 ( 1) 1 ( 1) , :@0.395737:0.697082:0.691443:0.697084:0.691443:0.681371:0.395737:0.681370:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.400541:0.697082:0.407996:0.697082:0.407996:0.681647:0.400541:0.681647:0.000000 2:@0.411880:0.696528:0.427213:0.696528:0.427213:0.682812:0.411880:0.682812:0.000000 2:@0.444769:0.691020:0.450005:0.691020:0.450005:0.681859:0.444769:0.681859:0.000000 1:@0.453915:0.696529:0.469249:0.696529:0.469249:0.682813:0.453915:0.682813:0.000000 2:@0.482241:0.700074:0.486654:0.700074:0.486654:0.674929:0.482241:0.674929:0.000000 dx:@0.491294:0.697084:0.507934:0.697084:0.507934:0.681648:0.491294:0.681648:0.000000:0.000000 5:@0.511836:0.696529:0.527170:0.696529:0.527170:0.682813:0.511836:0.682813:0.000000 1:@0.535623:0.689805:0.544606:0.689805:0.544606:0.674093:0.535623:0.674093:0.000000 12:@0.531132:0.706197:0.549098:0.706197:0.549098:0.690485:0.531132:0.690485:0.000000:0.000000 x:@0.569714:0.697086:0.577169:0.697086:0.577169:0.681651:0.569714:0.681651:0.000000 2:@0.581053:0.696531:0.596386:0.696531:0.596386:0.682816:0.581053:0.682816:0.000000 3:@0.613948:0.691020:0.619185:0.691020:0.619185:0.681859:0.613948:0.681859:0.000000 1 1:@0.623096:0.696529:0.668967:0.696529:0.668967:0.682813:0.623096:0.682813:0.000000:0.000000:0.000000 x:@0.642295:0.697084:0.649750:0.697084:0.649750:0.681648:0.642295:0.681648:0.000000 k:@0.672833:0.697084:0.680398:0.697084:0.680398:0.681648:0.672833:0.681648:0.000000 ;:@0.691351:0.696529:0.703628:0.696529:0.703628:0.682813:0.691351:0.682813:0.000000 x:@0.703536:0.697084:0.710991:0.697084:0.710991:0.681648:0.703536:0.681648:0.000000 [ 2, 3],:@0.710917:0.697084:0.782364:0.697084:0.782364:0.681371:0.710917:0.681371:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.714858:0.696794:0.729495:0.696794:0.729495:0.683384:0.714858:0.683384:0.000000 2:@0.734211:0.696529:0.749544:0.696529:0.749544:0.682813:0.734211:0.682813:0.000000 k:@0.323784:0.736802:0.331350:0.736802:0.331350:0.721367:0.323784:0.721367:0.000000 constante. Luego, :@0.331276:0.736802:0.503231:0.736807:0.503231:0.721094:0.331276:0.721089:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 [:@0.335230:0.736517:0.349867:0.736517:0.349867:0.723107:0.335230:0.723107:0.000000 R:@0.353736:0.735947:0.367026:0.735947:0.367026:0.723050:0.353736:0.723050:0.000000 P:@0.323788:0.776526:0.332550:0.776526:0.332550:0.761090:0.323788:0.761090:0.000000 ( 2) ( 2 1) 2 :@0.332476:0.776526:0.583554:0.776531:0.583554:0.760818:0.332476:0.760813:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2 5:@0.337280:0.775971:0.385507:0.775971:0.385507:0.762255:0.337280:0.762255:0.000000:0.000000:0.000000 1:@0.393961:0.769251:0.402944:0.769251:0.402944:0.753538:0.393961:0.753538:0.000000 12:@0.389470:0.785643:0.407435:0.785643:0.407435:0.769931:0.389470:0.769931:0.000000:0.000000 2 2:@0.412258:0.775977:0.455681:0.775977:0.455681:0.762262:0.412258:0.762262:0.000000:0.000000:0.000000 3:@0.473240:0.770467:0.478476:0.770467:0.478476:0.761306:0.473240:0.761306:0.000000 2 1 5 2:@0.482388:0.775976:0.579615:0.775976:0.579615:0.762260:0.482388:0.762260:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.533634:0.776531:0.541199:0.776531:0.541199:0.761095:0.533634:0.761095:0.000000 7:@0.588054:0.769251:0.597037:0.769251:0.597037:0.753538:0.588054:0.753538:0.000000 14:@0.583563:0.785643:0.601528:0.785643:0.601528:0.769931:0.583563:0.769931:0.000000:0.000000 1:@0.601547:0.775977:0.621390:0.775977:0.621390:0.762262:0.601547:0.762262:0.000000:0.000000 ,:@0.621298:0.776532:0.635950:0.776532:0.635950:0.760819:0.621298:0.760819:0.000000:0.000000:0.000000 k:@0.625255:0.776532:0.632820:0.776532:0.632820:0.761097:0.625255:0.761097:0.000000 P:@0.323781:0.816250:0.332543:0.816250:0.332543:0.800815:0.323781:0.800815:0.000000 (3) (3 1) 3 :@0.332469:0.816250:0.533873:0.816254:0.533873:0.800542:0.332469:0.800538:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.354908:0.815696:0.370241:0.815696:0.370241:0.801980:0.354908:0.801980:0.000000 1:@0.378720:0.808975:0.387703:0.808975:0.387703:0.793262:0.378720:0.793262:0.000000 12:@0.374229:0.825367:0.392194:0.825367:0.392194:0.809654:0.374229:0.809654:0.000000:0.000000 2:@0.409865:0.815701:0.425198:0.815701:0.425198:0.801985:0.409865:0.801985:0.000000 3:@0.442757:0.810190:0.447994:0.810190:0.447994:0.801030:0.442757:0.801030:0.000000 1 1 5:@0.451906:0.815700:0.529934:0.815700:0.529934:0.801984:0.451906:0.801984:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.503151:0.816254:0.510717:0.816254:0.510717:0.800819:0.503151:0.800819:0.000000 11:@0.533990:0.808975:0.551753:0.808975:0.551753:0.793262:0.533990:0.793262:0.000000:0.000000 3:@0.538371:0.825367:0.547354:0.825367:0.547354:0.809654:0.538371:0.809654:0.000000 1:@0.551864:0.815701:0.571707:0.815701:0.571707:0.801985:0.551864:0.801985:0.000000:0.000000 , y de la definición de función:@0.571615:0.816255:0.795705:0.816255:0.795705:0.800543:0.571615:0.800543:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.575572:0.816255:0.583138:0.816255:0.583138:0.800820:0.575572:0.800820:0.000000 primitiva:@0.323761:0.855974:0.391746:0.855974:0.391746:0.839304:0.323761:0.839304:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 se tiene::@0.391647:0.855974:0.455299:0.855974:0.455299:0.840261:0.391647:0.840261:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 #:@0.323781:0.898546:0.330294:0.898546:0.330294:0.876077:0.323781:0.876077:0.000000 3:@0.331869:0.883912:0.337585:0.883912:0.337585:0.873913:0.331869:0.873913:0.000000 2:@0.331869:0.901210:0.341626:0.901210:0.341626:0.892481:0.331869:0.892481:0.000000 2:@0.341568:0.901563:0.347284:0.901563:0.347284:0.891564:0.341568:0.891564:0.000000 f x dx:@0.348129:0.895701:0.386379:0.895701:0.386379:0.880266:0.348129:0.880266:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( ) (3) ( 2) :@0.352749:0.895701:0.525464:0.895701:0.525464:0.879989:0.352749:0.879989:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.390281:0.895146:0.405615:0.895146:0.405615:0.881431:0.390281:0.881431:0.000000 P:@0.409480:0.895701:0.418242:0.895701:0.418242:0.880266:0.409480:0.880266:0.000000 2 2 5:@0.440607:0.895146:0.521525:0.895146:0.521525:0.881431:0.440607:0.881431:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.459806:0.895701:0.468568:0.895701:0.468568:0.880266:0.459806:0.880266:0.000000 11:@0.525588:0.888422:0.543351:0.888422:0.543351:0.872709:0.525588:0.872709:0.000000:0.000000 3:@0.529969:0.904814:0.538952:0.904814:0.538952:0.889101:0.529969:0.889101:0.000000 1 2 2:@0.543462:0.895148:0.613188:0.895148:0.613188:0.881432:0.543462:0.881432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.563213:0.895703:0.578693:0.895703:0.578693:0.879990:0.563213:0.879990:0.000000:0.000000:0.000000 k:@0.567170:0.895703:0.574736:0.895703:0.574736:0.880267:0.567170:0.880267:0.000000 3:@0.593861:0.896285:0.597947:0.896285:0.597947:0.878631:0.593861:0.878631:0.000000 :@0.613096:0.895703:0.617127:0.895703:0.617127:0.879990:0.613096:0.879990:0.000000 17:@0.617268:0.888422:0.635031:0.888422:0.635031:0.872709:0.617268:0.872709:0.000000:0.000000 4:@0.621649:0.904814:0.630632:0.904814:0.630632:0.889101:0.621649:0.889101:0.000000 1:@0.635141:0.895148:0.654984:0.895148:0.654984:0.881432:0.635141:0.881432:0.000000:0.000000 :@0.654892:0.895703:0.693566:0.895703:0.693566:0.879990:0.654892:0.879990:0.000000:0.000000:0.000000:0.000000:0.000000 k:@0.658850:0.895703:0.666415:0.895703:0.666415:0.880267:0.658850:0.880267:0.000000 4:@0.666342:0.896285:0.670428:0.896285:0.670428:0.878631:0.666342:0.878631:0.000000 5:@0.674294:0.895148:0.689627:0.895148:0.689627:0.881432:0.674294:0.881432:0.000000 95:@0.693707:0.888422:0.711470:0.888422:0.711470:0.872709:0.693707:0.872709:0.000000:0.000000 12:@0.693596:0.904814:0.711562:0.904814:0.711562:0.889101:0.693596:0.889101:0.000000:0.000000 :@0.711580:0.895148:0.716182:0.895148:0.716182:0.881432:0.711580:0.881432:0.000000 ,:@0.716090:0.895703:0.719293:0.895703:0.719293:0.879990:0.716090:0.879990:0.000000 con lo que ( ) :@0.323776:0.935421:0.455222:0.935421:0.455222:0.919708:0.323776:0.919708:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a S:@0.405228:0.935421:0.427280:0.935421:0.427280:0.919986:0.405228:0.919986:0.000000:0.000000:0.000000 5:@0.435950:0.934866:0.451283:0.934866:0.451283:0.921151:0.435950:0.921151:0.000000 95:@0.455370:0.928145:0.473133:0.928145:0.473133:0.912433:0.455370:0.912433:0.000000:0.000000 12:@0.455259:0.944537:0.473225:0.944537:0.473225:0.928825:0.455259:0.928825:0.000000:0.000000 :@0.473243:0.934871:0.477845:0.934871:0.477845:0.921156:0.473243:0.921156:0.000000 .:@0.477753:0.935426:0.480956:0.935426:0.480956:0.919713:0.477753:0.919713:0.000000 Con respecto al cálculo :@0.082576:0.202047:0.239069:0.202047:0.239069:0.187763:0.082576:0.187763:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de áreas, sabemos que :@0.082576:0.217176:0.235858:0.217176:0.235858:0.202892:0.082576:0.202892:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el cálculo de algunas :@0.082576:0.232305:0.224067:0.232305:0.224067:0.218021:0.082576:0.218021:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 de ellas es sencillo (por :@0.082576:0.247434:0.236805:0.247434:0.236805:0.233150:0.082576:0.233150:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ejemplo, cuando en :@0.082576:0.262563:0.217503:0.262563:0.217503:0.248279:0.082576:0.248279:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 geometría nos referimos :@0.082576:0.277692:0.247309:0.277692:0.247309:0.263407:0.082576:0.263407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 al cálculo de cuadrados, :@0.082576:0.292821:0.243462:0.292821:0.243462:0.278536:0.082576:0.278536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 rectángulos, triángulos, :@0.082576:0.307950:0.239181:0.307950:0.239181:0.293665:0.082576:0.293665:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 círculos, etc). Otras áreas :@0.082576:0.323079:0.244464:0.323079:0.244464:0.308794:0.082576:0.308794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 son más complejas, y se :@0.082576:0.338207:0.243070:0.338207:0.243070:0.323923:0.082576:0.323923:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dividen en un número :@0.082576:0.353336:0.233318:0.353336:0.233318:0.339052:0.082576:0.339052:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 finito de triángulos.:@0.082576:0.368465:0.208960:0.368465:0.208960:0.354181:0.082576:0.354181:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Los antiguos griegos :@0.082576:0.383594:0.222103:0.383594:0.222103:0.369310:0.082576:0.369310:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fueron capaces de :@0.082576:0.398723:0.207077:0.398723:0.207077:0.384439:0.082576:0.384439:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 encontrar fórmulas para :@0.082576:0.413852:0.243445:0.413852:0.243445:0.399568:0.082576:0.399568:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 calcular áreas de regiones :@0.082576:0.428981:0.254702:0.428981:0.254702:0.414697:0.082576:0.414697:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (principalmente limitadas :@0.082576:0.444110:0.252963:0.444110:0.252963:0.429826:0.082576:0.429826:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 por cónicas) mediante el :@0.082576:0.459239:0.247426:0.459239:0.247426:0.444955:0.082576:0.444955:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 método de “exhaución” :@0.082576:0.474368:0.241278:0.474368:0.241278:0.460084:0.082576:0.460084:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (Arquímedes, 287-212 a. :@0.082576:0.489497:0.239640:0.489497:0.239640:0.475213:0.082576:0.475213:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 C.). En esencia, se trata de :@0.082576:0.504626:0.252634:0.504626:0.252634:0.490342:0.082576:0.490342:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 un proceso al límite, :@0.082576:0.519755:0.217401:0.519755:0.217401:0.505470:0.082576:0.505470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 donde la región en :@0.082576:0.534884:0.211587:0.534884:0.211587:0.520599:0.082576:0.520599:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 estudio queda encajada :@0.082576:0.550013:0.244273:0.550013:0.244273:0.535728:0.082576:0.535728:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 entre dos polígonos, :@0.082576:0.565142:0.221231:0.565142:0.221231:0.550857:0.082576:0.550857:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 uno inscrito y el otro :@0.082576:0.580271:0.220496:0.580271:0.220496:0.565986:0.082576:0.565986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 circunscrito, cuyas :@0.082576:0.595399:0.204869:0.595399:0.204869:0.581115:0.082576:0.581115:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 áreas respectivas se :@0.082576:0.610528:0.214762:0.610528:0.214762:0.596244:0.082576:0.596244:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 pueden calcular (no muy :@0.082576:0.625657:0.250385:0.625657:0.250385:0.611373:0.082576:0.611373:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 fácilmente, valga decirlo).:@0.082576:0.640786:0.247414:0.640786:0.247414:0.626502:0.082576:0.626502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Interdisciplinaria :@0.078581:0.141152:0.201990:0.141152:0.201990:0.125745:0.078581:0.125745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Matemática :@0.078581:0.156281:0.164074:0.156281:0.164074:0.141996:0.078581:0.141996:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 e historia:@0.078581:0.171410:0.138577:0.171410:0.138577:0.157125:0.078581:0.157125:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 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