37
Obtener el resultado de la sig. Integral ...._...__ .../.\..||/2 ...| ...|....sen(x)^2/sqrt(1-0.900601*sen(x)^2) dx ...| \_/.....0 ncs tol maxiter 6 0.0000005 50 Regla del rectangulo Limites de integracion a b 0 1.57079633 N Integral CC checar CC checar N i 1 0 0 2 0.52966005 1 Sigue Continuar 1 3 0.83802442 0.36796585 Sigue Continuar 2 4 1.02352216 0.18123471 Sigue Continuar 3 Regla del trapecio N Integral CC checar CC checar N i 1 2.49114424 0 2 1.77523217 0.403278 Sigue Continuar 1 3 1.66840583 0.06402899 Sigue Continuar 2 4 1.64630822 0.01342252 Sigue Continuar 3 5 1.64123975 0.0030882 Sigue Continuar 4 6 1.64002314 0.00074183 Sigue Continuar 5 7 1.63972373 0.00018259 Sigue Continuar 6 8 1.63964886 4.5661E-05 Sigue Continuar 7

7 - INTEGRACION_NUMERICA

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Page 1: 7 - INTEGRACION_NUMERICA

Obtener el resultado de la sig. Integral

...._...__

.../.\..||/2

...|

...|....sen(x)^2/sqrt(1-0.900601*sen(x)^2) dx

...|

\_/.....0

ncs tol maxiter6 0.0000005 50

Regla del rectangulo

Limites de integracion

a b N0 1.57079633 1

N Integral CC checar CC checar N i x1 0 0 02 0.52966005 1 Sigue Continuar 1 1.5707963273 0.83802442 0.36796585 Sigue Continuar 24 1.02352216 0.18123471 Sigue Continuar 3

Regla del trapecio W1

N Integral CC checar CC checar N i x1 2.49114424 0 02 1.77523217 0.403278 Sigue Continuar 1 1.5707963273 1.66840583 0.06402899 Sigue Continuar 24 1.64630822 0.01342252 Sigue Continuar 35 1.64123975 0.0030882 Sigue Continuar 46 1.64002314 0.00074183 Sigue Continuar 57 1.63972373 0.00018259 Sigue Continuar 68 1.63964886 4.56608E-05 Sigue Continuar 79 1.63962993 1.1547E-05 Sigue Continuar 8

10 1.6396251 2.94481E-06 Sigue Continuar 911 1.63962386 7.55969E-07 Sigue Continuar 10

Page 2: 7 - INTEGRACION_NUMERICA

12 1.63962354 1.95098E-07 Bien Continuar 1112

El resultado de resolver y evaluar la integral es 1.63962354

Utilizando las cifras cignificativas correctas el resultado es: 1.63962

Page 3: 7 - INTEGRACION_NUMERICA

☺ Chavez Tovar Angello Jair 2113033062

☺ González Pérez Ana Laura 2113001793

☺ Jiménez García Mayra Denisse 2113001195☺ Lozano Flores Marco Antonio 207366001

☺ Regalado Silva Roberto Carlos 207203156

H N H N H N H1.57079633 2 0.78539816 3 0.52359878 4 0.39269908

y x y x y x y0 0 0 0 0 0 0

3.17182335 0.78539816 0.67438412 0.52359878 0.28400845 0.392699081699 0.157178061.04719755 1.31650029 0.785398163397 0.67438412

1.178097245096 1.7748156

Z W Z W Z W Z1.57079633 2 0.78539816 3 0.52359878 4 0.39269908

y x y x y x y0 0 0 0 0 0 0

3.17182335 0.78539816 1.34876823 0.52359878 0.5680169 0.392699081699 0.314356131.57079633 3.17182335 1.04719755 2.63300058 0.785398163397 1.34876823

1.57079633 3.17182335 1.178097245096 3.54963121.570796326795 3.17182335

Page 4: 7 - INTEGRACION_NUMERICA

W Z W Z W Z W Z5 0.31415927 6 0.26179939 7 0.22439948 8 0.19634954

x y x y x y x y0 0 0 0 0 0 0 0

0.31415927 0.199766 0.26179939 0.13820842 0.22439948 0.10131592 0.19634954 0.077459590.62831853 0.83253985 0.52359878 0.5680169 0.44879895 0.41315984 0.39269908 0.31435613

0.9424778 2.04297376 0.78539816 1.34876823 0.67319843 0.9644177 0.58904862 0.726495131.25663706 4.20135379 1.04719755 2.63300058 0.8975979 1.82344354 0.78539816 1.348768231.57079633 3.17182335 1.30899694 4.6690364 1.12199738 3.13054872 0.9817477 2.25079048

1.57079633 3.17182335 1.34639685 5.00961861 1.17809725 3.54963121.57079633 3.17182335 1.37444679 5.26200209

1.57079633 3.17182335

Page 5: 7 - INTEGRACION_NUMERICA

W Z W Z W Z W Z9 0.17453293 10 0.15707963 11 0.14279967 12 0.13089969

x y x y x y x y0 0 0 0 0 0 0 0

0.17453293 0.06114331 0.15707963 0.04949191 0.14279967 0.04088159 0.13089969 0.034338630.34906585 0.24734712 0.31415927 0.199766 0.28559933 0.16474388 0.26179939 0.138208420.52359878 0.5680169 0.4712389 0.45678319 0.428399 0.37555456 0.39269908 0.31435613

0.6981317 1.04285048 0.62831853 0.83253985 0.57119866 0.68105834 0.52359878 0.56801690.87266463 1.70920629 0.78539816 1.34876823 0.71399833 1.09476306 0.65449847 0.908044211.04719755 2.63300058 0.9424778 2.04297376 0.856798 1.63922944 0.78539816 1.348768231.22173048 3.90292685 1.09955743 2.9740925 0.99959766 2.35042931 0.91629786 1.91268109

1.3962634 5.45246014 1.25663706 4.20135379 1.14239733 3.27829951 1.04719755 2.633000581.57079633 3.17182335 1.41371669 5.59876262 1.28519699 4.45414811 1.17809725 3.5496312

1.57079633 3.17182335 1.42799666 5.71304219 1.30899694 4.6690364

Page 6: 7 - INTEGRACION_NUMERICA

1.57079633 3.17182335 1.43989663 5.803697281.57079633 3.17182335

Page 7: 7 - INTEGRACION_NUMERICA

Encontrar el valor de la siguiente integral

...._...__

.../.\..||/2

...|

...|....sen(x)^2/sqrt(1-0,454276*sen(x)^2)dx ☺ Chavez Tovar Angello Jair

...| ☺ González Pérez Ana Laura\_/.....0 ☺ Jiménez García Mayra Denisse

☺ Lozano Flores Marco Antonio

Criterio de convergencia ☺ Regalado Silva Roberto CarlosNCS TOLERANCIA MAXITER

4 0.00005 50

regla de simpson

a b N H0 3.14159265 3 1.04719755

i x y0 0 0

N integral cc checar cc 1 1.04719755 2.771043131 2.17637219 2 2.0943951 2.771043132 1.93259488 0.12613989 3 3.14159265 1.50099E-323 1.95651837 0.01222758 44 1.953768 0.00140772 55 1.9541189 0.00017957 66 1.95407233 2.38359E-05 bien 7

89

101112131415161718

Page 8: 7 - INTEGRACION_NUMERICA

El resultado de la integral es: 1.95407233

Redondeando 1.954

Page 9: 7 - INTEGRACION_NUMERICA

211303306221130017932113001195

207366001

207203156

N H N H N H N H6 0.52359878 9 0.34906585 12 0.26179939 15 0.20943951

x y x y x y x y0 0 0 0 0 0 0 0

0.523598775598 0.79659724 0.34906585 0.36064655 0.26179939 0.20409121 0.20943951 0.130974171.047197551197 2.77104313 0.6981317 1.37529836 0.52359878 0.79659724 0.41887902 0.516075111.570796326795 2.70734417 1.04719755 1.84736209 0.78539816 1.13749376 0.62831853 0.752558582.094395102393 2.77104313 1.3962634 3.89004266 1.04719755 2.77104313 0.83775804 1.914223252.617993877991 0.79659724 1.74532925 3.89004266 1.30899694 3.6875613 1.04719755 2.77104313

3.14159265359 3.2104E-31 2.0943951 1.84736209 1.57079633 2.70734417 1.25663706 2.356930882.44346095 1.37529836 1.83259571 3.6875613 1.46607657 3.9985022

2.7925268 0.36064655 2.0943951 2.77104313 1.67551608 3.99850223.14159265 1.50099E-32 2.35619449 1.13749376 1.88495559 2.35693088

2.61799388 0.79659724 2.0943951 2.771043132.87979327 0.20409121 2.30383461 1.914223253.14159265 1.0341E-31 2.51327412 0.75255858

2.72271363 0.516075112.93215314 0.130974173.14159265 3.2104E-31

Page 10: 7 - INTEGRACION_NUMERICA

N H18 0.17453293

x y0 0

0.17453293 0.091087080.34906585 0.360646550.52359878 0.53106482

0.6981317 1.375298360.87266463 2.055667371.04719755 1.847362091.22173048 3.42317193

1.3962634 3.890042661.57079633 2.707344171.74532925 3.890042661.91986218 3.42317193

2.0943951 1.847362092.26892803 2.055667372.44346095 1.375298362.61799388 0.53106482

2.7925268 0.360646552.96705973 0.091087083.14159265 2.11639E-30

Page 11: 7 - INTEGRACION_NUMERICA

Encontrar el valor de la siguiente integral

...._...__ ☺ Chavez Tovar Angello Jair

.../.\..|| ☺ González Pérez Ana Laura

...| ☺ Jiménez García Mayra Denisse

...|....ln(11.1181+6.3618*cos(x)) dx ☺ Lozano Flores Marco Antonio

...| ☺ Regalado Silva Roberto Carlos

\_/.....0

NCS Tolerancia MaxIter3 0.0005 100

Regla del Rectangulo

a b max iter N1 H1 N20.00 3.1415927 50 1 3.1415927 2

Integral CC Checar CC i X Y X

8.9882588 0 0.00 2.8610516 0.008.2775093 0.0858652 1 3.1415927 1.5594701 1.57079637.9511635 0.0410438 2

7.7817234 0.0217741 3

7.6795664 0.0133024 4

7.6114212 0.008953 5

7.5627426 0.0064366 6

7.5262333 0.0048509 7

7.4978372 0.0037872 8

7.4751204 0.003039 9

7.4565338 0.0024927 10

7.441045 0.0020815 11

7.4279391 0.0017644 12

7.4167055 0.0015146 13

7.4069697 0.0013144 14

7.3984509 0.0011514 15

7.3909343 0.001017 16

7.3842528 0.0009048 17

7.3782747 0.0008102 18

7.3728944 0.0007297 19

7.3680265 0.0006607 20

7.3636011 0.000601 21

7.3595606 0.000549 22

7.3558567 0.0005035 23

7.3524492 0.0004635 correcto 24

Page 12: 7 - INTEGRACION_NUMERICA

☺ Chavez Tovar Angello Jair 2113033062☺ González Pérez Ana Laura 2113001793☺ Jiménez García Mayra Denisse 2113001195☺ Lozano Flores Marco Antonio 207366001

☺ Regalado Silva Roberto Carlos 207203156

H2 N3 H3 N4 H4 N5 H5 N6

1.5707963 3 1.0471976 4 0.7853982 5 0.6283185 6

Y X Y X Y X Y X

2.8610516 0.00 2.8610516 0.00 2.8610516 0.00 2.8610516 0.002.4085744 1.0471975512 2.6601896 0.7853982 2.7483327 0.6283185 2.7890097 0.5235988

2.09439510239 2.0715606 1.5707963 2.4085744 1.2566371 2.5713904 1.04719762.3561945 1.8900392 1.8849556 2.2139938 1.5707963

2.5132741 1.7869639 2.09439512.6179939

Page 13: 7 - INTEGRACION_NUMERICA

H6 N7 H7 N8 H8 N9 H9 N10

0.5235988 7 0.448799 8 0.3926991 9 0.3490659 10

Y X Y X Y X Y X

2.8610516 0.00 2.8610516 0.00 2.8610516 0.00 2.8610516 0.002.8110628 0.448799 2.8243438 0.3926991 2.8329567 0.3490659 2.8388584 0.31415932.6601896 0.8975979 2.7136755 0.7853982 2.7483327 0.6981317 2.7720587 0.62831852.4085744 1.3463969 2.5284237 1.1780972 2.6065825 1.0471976 2.6601896 0.94247782.0715606 1.7951958 2.2723801 1.5707963 2.4085744 1.3962634 2.5033043 1.25663711.7243046 2.2439948 1.9673337 1.9634954 2.1614298 1.7453293 2.3039227 1.5707963

2.6927937 1.6838617 2.3561945 1.8900392 2.0943951 2.0715606 1.88495562.7488936 1.656429 2.443461 1.8317297 2.1991149

2.7925268 1.637046 2.51327412.8274334

Page 14: 7 - INTEGRACION_NUMERICA

H10 N11 H11 N12 H12 N13 H13 N14

0.3141593 11 0.2855993 12 0.2617994 13 0.241661 14

Y X Y X Y X Y X

2.8610516 0.00 2.8610516 0.00 2.8610516 0.00 2.8610516 0.002.8430781 0.2855993 2.8461994 0.2617994 2.8485728 0.241661 2.8504196 0.22439952.7890097 0.5711987 2.8015397 0.5235988 2.8110628 0.4833219 2.8184695 0.4487992.6985029 0.856798 2.7268192 0.7853982 2.7483327 0.7249829 2.7650589 0.67319842.5713904 1.1423973 2.6218303 1.0471976 2.6601896 0.9666439 2.690023 0.89759792.4085744 1.4279967 2.4868613 1.3089969 2.54668 1.2083049 2.5933144 1.12199742.2139938 1.713596 2.3236341 1.5707963 2.4085744 1.4499658 2.4752712 1.34639691.9986012 1.9991953 2.1371576 1.8325957 2.248292 1.6916268 2.3371092 1.57079631.7869639 2.2847947 1.9390304 2.0943951 2.0715606 1.9332878 2.1817922 1.79519581.6228809 2.570394 1.7520156 2.3561945 1.8900392 2.1749488 2.015461 2.0195953

2.8559933 1.6122335 2.6179939 1.7243046 2.4166097 1.8494345 2.24399482.8797933 1.604038 2.6582707 1.7020182 2.4683942

2.8999317 1.5976006 2.69279372.9171932

Page 15: 7 - INTEGRACION_NUMERICA

H14 N15 H15 N16 H16 N17 H17 N18

0.2243995 15 0.2094395 16 0.1963495 17 0.1847996 18

Y X Y X Y X Y X

2.8610516 0.00 2.8610516 0.00 2.8610516 0.00 2.8610516 0.002.8518848 0.2094395 2.8530667 0.1963495 2.8540339 0.1847996 2.8548354 0.17453292.8243438 0.418879 2.8290809 0.3926991 2.8329567 0.3695991 2.8361679 0.34906592.7783195 0.6283185 2.7890097 0.5890486 2.7977534 0.5543987 2.8049961 0.52359882.7136755 0.837758 2.7327412 0.7853982 2.7483327 0.7391983 2.7612451 0.69813172.6303323 1.0471976 2.6601896 0.9817477 2.6846128 0.9239978 2.7048411 0.87266462.5284237 1.2566371 2.5713904 1.1780972 2.6065825 1.1087974 2.6357517 1.04719762.4085744 1.4660766 2.4666654 1.3744468 2.5144028 1.293597 2.5540509 1.22173052.2723801 1.6755161 2.3468996 1.5707963 2.4085744 1.4783965 2.460024 1.39626342.1231974 1.8849556 2.2139938 1.7671459 2.2902062 1.6631961 2.3543335 1.57079631.9673337 2.0943951 2.0715606 1.9634954 2.1614298 1.8479957 2.2382717 1.74532931.8155158 2.3038346 1.925886 2.1598449 2.0259977 2.0327952 2.114133 1.91986221.6838617 2.5132741 1.7869639 2.3561945 1.8900392 2.2175948 1.9857157 2.09439511.5924552 2.7227136 1.668896 2.552544 1.7627522 2.4023944 1.8588998 2.268928

2.9321531 1.5882798 2.7488936 1.656429 2.587194 1.7420769 2.4434612.9452431 1.584846 2.7719935 1.6459431 2.6179939

2.9567931 1.581989 2.79252682.9670597

Page 16: 7 - INTEGRACION_NUMERICA

H18 N19 H19 N20 H20 N21 H21 N22

0.1745329 19 0.165347 20 0.1570796 21 0.1495997 22

Y X Y X Y X Y X

2.8610516 0.00 2.8610516 0.00 2.8610516 0.00 2.8610516 0.002.8555071 0.165347 2.8560755 0.1570796 2.8565608 0.1495997 2.8569784 0.14279972.8388584 0.330694 2.8411348 0.3141593 2.8430781 0.2991993 2.8447502 0.28559932.8110628 0.4960409 2.816195 0.4712389 2.8205753 0.448799 2.8243438 0.4283992.7720587 0.6613879 2.7812049 0.6283185 2.7890097 0.5983986 2.7957232 0.57119872.7217812 0.8267349 2.7361082 0.7853982 2.7483327 0.7479983 2.7588466 0.71399832.6601896 0.9920819 2.6808623 0.9424778 2.6985029 0.8975979 2.7136755 0.8567982.5873101 1.1574289 2.6154674 1.0995574 2.639507 1.0471976 2.6601896 0.99959772.5033043 1.3227759 2.5400125 1.2566371 2.5713904 1.1967972 2.5984084 1.14239732.4085744 1.4881228 2.4547441 1.4137167 2.4943044 1.3463969 2.5284237 1.2851972.3039227 1.6534698 2.3601695 1.5707963 2.4085744 1.4959965 2.4504461 1.42799672.1907857 1.8188168 2.257208 1.727876 2.3147997 1.6455962 2.3648725 1.57079632.0715606 1.9841638 2.1474032 1.8849556 2.2139938 1.7951958 2.2723801 1.713596

1.950018 2.1495108 2.0332045 2.0420352 2.1077743 1.9447955 2.1740553 1.85639571.8317297 2.3148577 1.9182996 2.1991149 1.9986012 2.0943951 2.0715606 1.99919531.7243046 2.4802047 1.8079192 2.3561945 1.8900392 2.2439948 1.9673337 2.141995

1.637046 2.6455517 1.7089328 2.5132741 1.7869639 2.3935944 1.8647885 2.28479471.5795868 2.8108987 1.6294366 2.6703538 1.6955596 2.5431941 1.7684455 2.4275943

2.9762457 1.5775481 2.8274334 1.6228809 2.6927937 1.6838617 2.5703942.984513 1.5758034 2.8423934 1.6171951 2.7131937

2.991993 1.5742989 2.85599332.998793

Page 17: 7 - INTEGRACION_NUMERICA

H22 N23 H23 N24 H24 N25 H25

0.1427997 23 0.136591 24 0.1308997 25 0.1256637

Y X Y X Y X Y

2.8610516 0.00 2.8610516 0.00 2.8610516 0.00 2.86105162.8573403 0.136591 2.857656 0.1308997 2.8579332 0.1256637 2.85817772.8461994 0.273182 2.8474635 0.2617994 2.8485728 0.2513274 2.84955162.8276092 0.409773 2.8304575 0.3926991 2.8329567 0.3769911 2.83516162.8015397 0.5463639 2.8066124 0.5235988 2.8110628 0.5026548 2.81498872.7679547 0.6829549 2.775897 0.6544985 2.7828642 0.6283185 2.78900972.7268192 0.8195459 2.7382798 0.7853982 2.7483327 0.7539822 2.75719922.6781097 0.9561369 2.6937366 0.9162979 2.7074446 0.8796459 2.71953492.6218303 1.0927279 2.6422623 1.0471976 2.6601896 1.0053096 2.67600372.5580352 1.2293189 2.5838871 1.1780972 2.6065825 1.1309734 2.62661042.4868613 1.3659098 2.5186997 1.3089969 2.54668 1.2566371 2.57139042.4085744 1.5025008 2.4468798 1.4398966 2.4806042 1.3823008 2.51042682.3236341 1.6390918 2.3687431 1.5707963 2.4085744 1.5079645 2.44387292.2327819 1.7756828 2.2848033 1.701696 2.3309508 1.6336282 2.37198422.1371576 1.9122738 2.1958528 1.8325957 2.248292 1.7592919 2.29515932.0384439 2.0488648 2.1030675 1.9634954 2.1614298 1.8849556 2.21399381.9390304 2.1854558 2.0081302 2.0943951 2.0715606 2.0106193 2.1293474

1.842163 2.3220467 1.9133624 2.2252948 1.9803504 2.136283 2.04242441.7520156 2.4586377 1.8218327 2.3561945 1.8900392 2.2619467 1.95486081.6735769 2.5952287 1.7373833 2.4870942 1.8035142 2.3876104 1.8688051.6122335 2.7318197 1.6644913 2.6179939 1.7243046 2.5132741 1.78696391.5729926 2.8684107 1.6078793 2.7488936 1.656429 2.6389378 1.7125741

3.0050017 1.5718511 2.8797933 1.604038 2.7646015 1.64924463.010693 1.570848 2.8902652 1.6006328

3.0159289 1.5699618

Page 18: 7 - INTEGRACION_NUMERICA

Encontrar el valor de la siguiente integral

...._...__

.../.\..||

...|

...|....ln(11.1181+6.3618*cos(x)) dx ☺ Chavez Tovar Angello Jair

...| ☺ González Pérez Ana Laura

\_/.....0 ☺ Jiménez García Mayra Denisse☺ Lozano Flores Marco Antonio

NCS Tolerancia MaxIter ☺ Regalado Silva Roberto Carlos

4 0.00005 100

Regla del Trapecio

a b N10.00 3.1415927 1

N Integral CC Checar CC i X1 6.9437393 0 0.002 7.2552495 0.0429358 1 3.14159273 7.2696569 0.0019819 24 7.2705935 0.0001288 35 7.2706625 9.4924E-06 Correcto 4

5

Page 19: 7 - INTEGRACION_NUMERICA

211303306221130017932113001195

207366001

207203156

H1 N2 H2 N3 H3 N4 H4

3.14159265359 2 1.5707963 3 1.0471976 4 0.7853982

Y X Y X Y X Y2.861051649387 0.00 2.8610516 0.00 2.8610516 0.00 2.86105161.559470055056 1.5707963 4.8171488 1.0471976 5.3203792 0.7853982 5.4966653

3.1415927 1.5594701 2.0943951 4.1431211 1.5707963 4.81714883.1415927 1.5594701 2.3561945 3.7800784

3.1415927 1.5594701

Page 20: 7 - INTEGRACION_NUMERICA

N5 H55 0.6283185

X Y0.00 2.8610516

0.6283185 5.57801941.2566371 5.14278091.8849556 4.42798762.5132741 3.57392793.1415927 1.5594701

Page 21: 7 - INTEGRACION_NUMERICA

Encontrar el valor de la siguiente integral

...._...__

.../.\..|| ☺ Chavez Tovar Angello Jair

...| ☺ González Pérez Ana Laura

...|....ln(11.1181+6.3618*cos(x)) dx ☺ Jiménez García Mayra Denisse

...| ☺ Lozano Flores Marco Antonio

\_/.....0 ☺ Regalado Silva Roberto Carlos

NCS Tolerancia MaxIter

4 0.00005 100

Regla de Simpson 1/3

a b N20.00 3.1415927 2

N Integral CC Checar CC i X2 7.3590862 0 0.004 7.2757081 0.0114598 1 1.57079636 7.2710049 0.0006468 2 3.14159278 7.2706934 4.2847E-05 correcto 3

45678

Page 22: 7 - INTEGRACION_NUMERICA

211303306221130017932113001195

207366001

207203156

H2 N4 H4 N6 H6 N8 H8

1.5707963267949 4 0.7853982 6 0.5235988 8 0.3926991

Y X Y X Y X Y2.8610516493872 0.00 2.8610516 0.00 2.8610516 0.00 2.86105169.6342976436571 0.7853982 10.993331 0.5235988 11.244251 0.3926991 11.3318271.5594700550562 1.5707963 4.8171488 1.0471976 5.3203792 0.7853982 5.4966653

2.3561945 7.5601567 1.5707963 9.6342976 1.1780972 10.426333.1415927 1.5594701 2.0943951 4.1431211 1.5707963 4.8171488

2.6179939 6.8972185 1.9634954 8.64571923.1415927 1.5594701 2.3561945 3.7800784

2.7488936 6.62571593.1415927 1.5594701

Page 23: 7 - INTEGRACION_NUMERICA

Encontrar el valor de la siguiente integral

...._...__

.../.\..||

...| ☺ Chavez Tovar Angello Jair

...|....ln(11.1181+6.3618*cos(x)) dx ☺ González Pérez Ana Laura

...| ☺ Jiménez García Mayra Denisse

\_/.....0 ☺ Lozano Flores Marco Antonio

☺ Regalado Silva Roberto Carlos

NCS Tolerancia MaxIter

4 0.00005 100

Regla de Simpson 3/8

a b N3 H30.00 3.1415927 3 1.0471976

N Integral CC Checar CC i X Y

3 7.3103967 0 0.00 2.8610516

6 7.2725952 0.0051978 1 1.0471976 7.9805688

9 7.2707948 0.0002476 2 2.0943951 6.2146817

12 7.2706778 1.6101E-05 correcto 3 3.1415927 1.5594701456789

101112

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211303306221130017932113001195

207366001

207203156

N6 H6 N9 H9 N12 H126 0.5235988 9 0.3490659 12 0.2617994

X Y X Y X Y

0.00 2.8610516 0.00 2.8610516 0.00 2.86105160.523598776 8.4331884 0.3490659 8.5165751 0.2617994 8.54571851.047197551 7.9805688 0.6981317 8.316176 0.5235988 8.43318841.570796327 4.8171488 1.0471976 5.3203792 0.7853982 5.49666532.094395102 6.2146817 1.3962634 7.5099129 1.0471976 7.98056882.617993878 5.1729139 1.7453293 6.9117681 1.3089969 7.64004013.141592654 1.5594701 2.0943951 4.1431211 1.5707963 4.8171488

2.443461 5.495189 1.8325957 6.74487612.7925268 4.9111379 2.0943951 6.21468173.1415927 1.5594701 2.3561945 3.7800784

2.6179939 5.17291392.8797933 4.81211393.1415927 1.5594701

Page 25: 7 - INTEGRACION_NUMERICA

Encontrar el valor de la siguiente integral...._...__.../.\..||/2...| ☺ Chavez Tovar Angello Jair

...|....cos(x)/sqrt(1-0.435732*sen(x)^2) dx ☺ González Pérez Ana Laura

...| ☺ Jiménez García Mayra Denisse

\_/.....0 ☺ Lozano Flores Marco Antonio

☺ Regalado Silva Roberto Carlos

Criterio de convergencia

NCS Tol MaxIter4 0.00005 50

Limites de integracion

a b0 1.57079633

Regla del RectanguloN1

N Integral CC Checar CC Checar N i X1 1.57079633 0 02 1.41336152 0.11139033 Sigue Continua 1 1.570796333 1.32304433 0.06826467 Sigue Continua 24 1.27127175 0.04072503 Sigue Continua 35 1.23825431 0.02666451 Sigue Continua 4

Regla del TrapecioN1

N Integral CC Checar CC Checar N i X1 0.78539816 0 02 1.02066244 0.23050155 Sigue Continua 1 1.570796333 1.06124494 0.03824047 Sigue Continua 24 1.07492221 0.01272396 Sigue Continua 35 1.08117468 0.00578303 Sigue Continua 46 1.08455277 0.00311473 Sigue Continua 57 1.08658375 0.00186915 Sigue Continua 68 0.98972486 0.09786446 Sigue Continua 7

8

Page 26: 7 - INTEGRACION_NUMERICA

Regla de Simpson de 1/3N2

N Integral CC Checar CC Checar N i X2 1.09908386 0 04 1.0930088 0.00555811 Sigue Continua 1 0.785398166 1.09232204 0.00062872 Sigue Continua 2 1.570796338 1.09222544 8.84477E-05 Sigue Continua 3

10 1.09220153 2.18859E-05 Bien Continua 456789

10

El resultado de la integral es: 1.09220153

REDONDEANDO: 1.092

Regla de Simpson de 1/3N3

N Integral CC Checar CC Checar N i X3 1.09572579 0 06 1.09253906 0.00291682 Sigue Continua 1 0.523598789 1.09224523 0.00026901 Sigue Continua 2 1.04719755

12 1.09220328 3.8415E-05 Bien Continua 3 1.57079633456789

101112

El resultado de la integral es: 1.09220328

REDONDEANDO: 1.092

Page 27: 7 - INTEGRACION_NUMERICA

☺ Chavez Tovar Angello Jair 2113033062

☺ González Pérez Ana Laura 2113001793

☺ Jiménez García Mayra Denisse 2113001195

☺ Lozano Flores Marco Antonio 207366001

☺ Regalado Silva Roberto Carlos 207203156

H N H N H N H1.57079633 2 0.78539816 3 0.52359878 4 0.39269908

Y X Y X Y X Y1 0 1 0 1 0 1

8.15485E-17 0.785398163397 0.79954778 0.52359878 0.91743531 0.39269908 0.954846781.04719755 0.60939323 0.78539816 0.79954778

1.17809725 0.48287238

H N H N H N H1.57079633 2 0.78539816 3 0.52359878 4 0.39269908

Y X Y X Y X Y1 0 1 0 1 0 1

8.15485E-17 0.785398163397 1.59909555 0.52359878 1.83487062 0.39269908 1.909693561.570796326795 8.15485E-17 1.04719755 1.21878647 0.78539816 1.59909555

1.57079633 8.15485E-17 1.17809725 0.965744751.57079633 8.15485E-17

Page 28: 7 - INTEGRACION_NUMERICA

H N H N H N H0.78539816 4 0.39269908 6 0.26179939 8 0.19634954

Y X Y X Y X Y1 0 1 0 1 0 1

3.1981911 0.392699081699 3.81938713 0.26179939 3.9213564 0.19634954 3.956082228.15485E-17 0.785398163397 1.59909555 0.52359878 1.83487062 0.39269908 1.90969356

1.178097245096 1.9314895 0.78539816 3.1981911 0.58904862 3.574957661.570796326795 8.15485E-17 1.04719755 1.21878647 0.78539816 1.59909555

1.30899694 1.34388397 0.9817477 2.65848891.57079633 3.77144E-16 1.17809725 0.96574475

1.37444679 1.023912751.57079633 8.15485E-17

H N H N H N H0.52359878 6 0.26179939 9 0.17453293 12 0.13089969

Y X Y X Y X Y1 0 1 0 1 0 1

2.75230593 0.261799387799 2.9410173 0.17453293 2.97402561 0.13089969 2.985436581.8281797 0.523598775598 2.75230593 0.34906585 2.89379206 0.26179939 2.9410173

8.15485E-17 0.785398163397 1.59909555 0.52359878 1.83487062 0.39269908 1.909693561.047197551197 1.8281797 0.6981317 2.53791627 0.52359878 2.752305931.308996938996 1.00791298 0.87266463 2.23518857 0.65449847 2.599146221.570796326795 3.77144E-16 1.04719755 1.21878647 0.78539816 1.59909555

1.22173048 1.30813036 0.91629786 2.143759281.3962634 0.68556792 1.04719755 1.8281797

1.57079633 8.15485E-17 1.17809725 0.965744751.30899694 1.007912981.43989663 0.517890591.57079633 -2.1405E-16

Page 29: 7 - INTEGRACION_NUMERICA

N H5 0.31415927

X Y0 1

0.31415927 0.971482310.62831853 0.87778188

0.9424778 0.695221931.25663706 0.39699975

N H N H N H N H5 0.31415927 6 0.26179939 7 0.22439948 8 0.19634954

X Y X Y X Y X Y0 1 0 1 0 1 0 1

0.31415927 1.94296461 0.26179939 1.9606782 0.22439948 1.97123701 0.19634954 1.978041110.62831853 1.75556377 0.52359878 1.83487062 0.44879895 1.88072477 0.39269908 1.90969356

0.9424778 1.39044387 0.78539816 1.59909555 0.67319843 1.71570886 0.58904862 1.787478831.25663706 0.79399951 1.04719755 1.21878647 0.8975979 1.45583994 0.78539816 1.599095551.57079633 8.15485E-17 1.30899694 0.67194198 1.12199738 1.07941234 0.9817477 1.32924445

1.57079633 3.77144E-16 1.34639685 0.5814469 1.17809725 0.965744751.57079633 8.15485E-17 1.37444679 0.51195637

1.57079633 8.15485E-17

Page 30: 7 - INTEGRACION_NUMERICA

N H10 0.15707963

X Y0 1

0.15707963 3.971987010.31415927 1.94296461

0.4712389 3.735719570.62831853 1.755563770.78539816 3.1981911

0.9424778 1.390443871.09955743 2.24539521.25663706 0.793999511.41371669 0.825248081.57079633 8.15485E-17