Problem: `int_(0)^( pi)(cos theta+sin theta)d theta`

int_0^(pi//2)(theta/sintheta)^2d theta=

The value of the integral int_(0)^(2pi)(sin2 theta)/(a-b cos theta)d theta when a gt b gt 0 , is

Evaluate: int_0^(pi//2)sqrt(costheta)sin^3theta d theta

6) int_0^(pi/4)sec^4theta d theta

6) int_0^(pi/4)sec^4theta d theta

5. int_0^(pi/4)sec^2theta d theta

9. int_0^(pi/2)sec^4theta d theta

int_0^(pi/2) sqrt(sintheta)cos^5theta d theta

Evaluate int_(0)^(pi//2) cos theta tan ^(-1) ( sin theta)d theta .

Let f beintegrable over [0,a] for any real value of a . If I_(1)=int_(0)^(pi//2)cos theta f(sin theta +cos^(2) theta) d theta and I_(2)=int_(0)^(pi//2) sin 2 theta f(sin theta+cos^(2) theta) d theta , then