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

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Answer 1 · 2016-07-30T12:35:22

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

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

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

$=int1du - intcos(u)du$

$=u - sin(u) + C$

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

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