`int_0^(pi/2) (a+bsintheta)^3costheta d theta`

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

int_(0)^( pi/2) sin^(2)theta cos theta d theta

Evaluate the following integral: int_0^(pi//2)(sintheta)/(sqrt(1+costheta))d theta

If I=int_0^a (dx)/(sqrt(x+a)+sqrtx)=int_0^(pi/8) (2tantheta)/(sin2theta) d(theta),(where a>0) (A) a=3/4 (B) cot((3pi)/8) (C) tan((3pi)/8) (D) tan(pi/8)

int _(0) ^(pi) sin ^(2) theta cos theta d theta

int_0^(pi/4) (2sinthetacostheta)/(sin^4theta+cos^4theta)d theta

Prove that int_(0)^(2pi)e^(costheta)cos(sintheta)d theta=2pi .

Show that int_(0)^(2)sqrt((sin2 theta))sin theta d theta=(pi)/(4)

int_(0)^(pi//3)(costheta)/(5-4sintheta)d theta equal to