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`

If int_0^(pi/2)logsinthetadtheta=k , then find the value of int_pi^(pi/2)(theta/(s intheta))^2dtheta in terms of k

Find the value of int_0^(pi/2)sin2xlogtanxdx

Evaluate: int_0^(pi/2)[cost]dt

Evaluate: int_(0)^(pi/2)(costheta)/((1+sintheta)(2+sintheta))d theta .

Evaluate int_(0)^(pi//2)(costheta)/((1+sintheta)(2+sintheta))d theta

Evaluate: int_(0)^(pi//2) sqrtsinthetacos^(5)theta d theta

Evaluate: int_0^(pi/2)xcotx dx

Iflambda=int_0^(pi/2)costhetaf(sintheta+cos^2theta)dtheta a n dI_2=int_0^(pi//2)sin2thetaf(sintheta+cos^2theta)dtheta,t h e n I_1=-2I_2 (b) I_1=I_2 2I_1=I_2 (d) I_1=-I_2

Show that int_0^(pi/2)sqrt((sin2theta))sinthetadtheta=pi/4