Question

How do you find the antiderivative of `(sinx)^2`?

Answer 1

`= x/2 -1/4 sin 2x + C`

Explanation:

us the identity `cos 2A = 1 - 2 sin^2 A implies sin^2 A = 1/2(1-cos 2A)`

so

`int dx qquad sin^2 x`

`= 1/2 int dx qquad 1 - cos 2x`

`= 1/2 (x -1/2 sin 2x) + C`

`= x/2 -1/4 sin 2x + C`