Question

How do you find the integral of `sin^2 (x/4)`?

Answer 1

`intsin^2(x/4)dx=x/2 - sin(x/2) + C`

Explanation:

First, we apply the power reduction formula `sin^2(x) = (1-cos(2x))/2`

`intsin^2(x/4)dx = int(1-cos(x/2))/2dx`

Next, we make the substitution `u = x/2`. Then `du = 1/2dx`, so we get

`int(1-cos(x/2))/2dx = int(1-cos(u))du`

`=int1du - intcos(u)du`

`=u - sin(u) + C`

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