Tutorial to find integrals involving even powers of sin(x), using reducing power formulas, are presented. Exercises with answers are at the bottom of the page. Integrating odd powers of sine is much simpler.
Exercises: Evaluate the following integrals.
(a) [ 8 sin6(x) - 2 sin2(x) ]dx
(b) [ 4 sin4(x) + sin2(x) ]dx
Answers to Above Exercises
(a) (3/2)x - (11/8) sin(2x) + (3/8)sin(4x) - (1/24) sin(6x) + C
(b) 2x - (5/4)sin(2x) + (1/8) sin(4x) + C
More references on
integrals and their applications in calculus.