1/5 / | | -9 | ------ dx | cos(x) | / 0
Integral(-9/cos(x), (x, 0, 1/5))
/ | | -9 | ------ dx | cos(x) | /
-9 ------ cos(x)
cos(x)
-9 -9*cos(x) ------ = --------- cos(x) 2 cos (x)
sin(a)^2 + cos(a)^2 = 1
2 2 cos (x) = 1 - sin (x)
-9*cos(x) -9*cos(x) --------- = ----------- 2 2 cos (x) 1 - sin (x)
u = sin(x)
/ | | -9*cos(x) | ----------- dx | 2 = | 1 - sin (x) | /
/ | | -9*cos(x) | ----------- dx | 2 = | 1 - sin (x) | /
/ | | -9 | ------ du | 2 | 1 - u | /
-9 -9 / 1 1 \ ------ = ---*|----- + -----| 2 2 \1 - u 1 + u/ 1 - u
/ / | | | 1 | 1 9* | ----- du 9* | ----- du / | 1 + u | 1 - u | | | | -9 / / = | ------ du = - ------------- - ------------- | 2 2 2 | 1 - u | /
= -9*log(1 + u)/2 + 9*log(-1 + u)/2
u = sin(x)
/ | | -9 9*log(1 + sin(x)) 9*log(-1 + sin(x)) | ------ dx = - ----------------- + ------------------ + C0 | cos(x) 2 2 | /
/ | | -9 9*log(1 + sin(x)) 9*log(-1 + sin(x)) | ------ dx = C - ----------------- + ------------------ | cos(x) 2 2 | /
9*log(1 + sin(1/5)) 9*log(1 - sin(1/5)) - ------------------- + ------------------- 2 2
=
9*log(1 + sin(1/5)) 9*log(1 - sin(1/5)) - ------------------- + ------------------- 2 2
-9*log(1 + sin(1/5))/2 + 9*log(1 - sin(1/5))/2
Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.