# trig integration

posted by
**christine**
.

s- integral

endpoints are 0 and pi/2

i need to find the integral of sin^2 (2x) dx.

i know that the answer is pi/4, but im not sure how to get to it.

i know:

s sin^2(2x)dx= 1/2 [1-cos (4x)] dx, but then i'm confused.

The indefinite integral of

(1/2) [1-cos (4x)] is

(x/2) - (1/2)(1/4)(sin 4x)

Evaluate that at x = p/2 and 0 and take the difference

I get [(pi/4) -0] - {0 - 0) = pi/4

YOu got the hardest part, now expand your expression.

Hint: what is the derivative of 1/8 sin(4x)?