# Primitive of Square of Sine of a x

Jump to navigation Jump to search

## Theorem

$\displaystyle \int \sin^2 a x \rd x = \frac x 2 - \frac {\sin 2 a x} {4 a} + C$

## Proof

 $\displaystyle \int \sin^2 x \rd x$ $=$ $\displaystyle \frac x 2 - \frac {\sin 2 x} 4 + C$ Primitive of $\sin^2 x$ $\displaystyle \leadsto \ \$ $\displaystyle \int \sin^2 a x \rd x$ $=$ $\displaystyle \frac 1 a \paren {\frac {a x} 2 - \frac {\sin 2 a x} 4} + C$ Primitive of Function of Constant Multiple $\displaystyle$ $=$ $\displaystyle \frac x 2 - \frac {\sin 2 a x} {4 a} + C$ simplifying

$\blacksquare$