int_(0)^( pi)5(5-4cos theta)^(1/4)sin theta d theta

Evaluate the following integrals by changing the limits of integration after suitable subsitutions: underset(0)overset(pi)int5(5-4cos theta)^(1//4) sin theta d theta

[ (A) 8/5, (B) 5/8int_(0)^(2 pi)(sin2 theta)/(a-b cos theta)d theta equals- [ (A) 1, (B) 2, (C) pi/4]]

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

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

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