Primitive integral

=2∫(0,pi/2)sin^6xdx

= 2[(5 * 3 * 1)/(6 * 4 * 2)](pi/2)= 15pi/48 = 5pi/ 16

Generally, for j = ∫ (0, pi/2) sin n (x) dx = ∫ (0, pi/2) cos n (x) dx = {[(n- 1)! ! ]/(n！ ! )}J*

When n is odd, J*= 1. When n is an even number, J*=pi/2.