What is the antiderivative of sin^2 3x ?

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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To determine the antiderivative of the given function, we'll have to integrate the function.

`int` (sin 3x)^2 dx

We'll use the half angle identity:

(sin a)^2 = (1-cos 2a)/2

We'll re-write the inetgral:

`int` (sin 3x)^2 dx = `int` (1 - cos 6x) dx/2

`int` (1 - cos 6x) dx/2 = `int` dx/2 - (1/2)*`int` cos 6x dx

`int` (1 - cos 6x) dx/2 = x/2 - sin 6x/12 + C

The antiderivative of the given function is the primitive function F(x)= x/2 - sin 6x/12 + C.

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