`int_(0)^( pi/2)(cos theta+sin theta)^(2)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

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

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

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

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

If int_0^(pi/2)logsinthetad theta=k , then find the value of int_0^(pi/2)(theta/(sintheta))^2d theta in terms of k

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

If int_0^(pi/2)logsinthetad(theta)=k , then find the value of int_0^(pi/2)(theta/(sintheta))^2d(theta) in terms of k

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4

Show that int_0^(pi/2)sqrt((sin2theta))sintheta d theta=pi/4