EJERCICIOS INTEGRACIÓN NUMÉRICA

Integración por el Método de los Rectángulos

Errror

VALOR VERDADERO 1

a 0 n 30b 1.57079633 h 0.05235988

xi f(xi) f(x)i 0 0 00 0.05235988 0.05233596 0.052335961 0.10471976 0.10452846 0.104528462 0.15707963 0.15643447 0.156434473 0.20943951 0.20791169 0.207911694 0.26179939 0.25881905 0.258819055 0.31415927 0.30901699 0.309016996 0.36651914 0.35836795 0.358367957 0.41887902 0.40673664 0.406736648 0.4712389 0.4539905 0.45399059 0.52359878 0.5 0.5

10 0.57595865 0.54463904 0.5446390411 0.62831853 0.58778525 0.5877852512 0.68067841 0.62932039 0.6293203913 0.73303829 0.66913061 0.6691306114 0.78539816 0.70710678 0.70710678

〖=[−𝐶𝑜𝑠(𝑥)]〗 _0^(𝜋/2)=−𝐶𝑜𝑠(𝜋/2)+𝐶𝑜𝑠(0)ℎ=(( − )" 𝑏 𝑎 " )/𝑛

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1

1.2

f(xi)

∫25_0^(𝜋/2)▒〖 sin (𝑥)𝑑𝑥〗

∫25_(𝑥_0)^(𝑥_0+ℎ)▒〖𝑓 (𝑥)𝑑𝑥=ℎ𝑓(𝑥_0)〗∫25_𝑎^𝑏▒〖𝑓 (𝑥)𝑑𝑥=ℎ∑24_0^(𝑛−1)▒〖𝑓 ( _𝑥 𝑖)〗〗

ℎ/2 (𝑏−𝑎) 𝑓^′ (𝑢), 𝑐𝑜𝑛 𝜇 𝜖(𝑎,𝑏)

15 0.83775804 0.74314483 0.7431448316 0.89011792 0.77714596 0.7771459617 0.9424778 0.80901699 0.8090169918 0.99483767 0.83867057 0.8386705719 1.04719755 0.8660254 0.866025420 1.09955743 0.89100652 0.8910065221 1.15191731 0.91354546 0.9135454622 1.20427718 0.93358043 0.9335804323 1.25663706 0.95105652 0.9510565224 1.30899694 0.96592583 0.9659258325 1.36135682 0.9781476 0.978147626 1.41371669 0.98768834 0.9876883427 1.46607657 0.9945219 0.994521928 1.51843645 0.99862953 0.9986295329 1.57079633 130

Sumatoria 18.5942296

h*sumatoria 0.97359159 Estimación de la Integral

Error 0.02640841

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.80

0.2

0.4

0.6

0.8

1

1.2

f(xi)