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

Evaluate the following : int_(0)^(pi//2)sin theta d theta

Prove that int_0^(pi/2)(costheta-sintheta)/(1+sintheta.costheta)d theta=0.

Evaluate int_0^(pi/4)sqrt(1+tan^2theta)d theta.

If int_(0)^((pi)/(2))log sin theta d(theta)=k, then find the value of int_(0)^((pi)/(2))((theta)/(sin theta))^(2)d(theta) in terms of k

What is int_0^(pi//2) (d theta)/(1+ cos theta) equal to

If f(x)=int_(0)^((pi)/(2))(ln(1+x sin^(2)theta))/(sin^(2)theta)d theta,x>=0 then :