Question

What is the antiderivative of `sin^2(x)`?

Answer 1

`= 1/2[x - 1/2sin2x] + C`

Explanation:

We're going to use the trig identity

`cos2theta = 1 -2sin^2theta`

`implies sin^2x = 1/2(1 - cos2x)`

So `int sin^2xdx = 1/2int(1-cos2x)dx`

`= 1/2[x - 1/2sin2x] + C`