# Primitive of Sine Function/Corollary

(Redirected from Primitive of Sine of a x)

## Corollary to Primitive of Sine Function

$\displaystyle \int \sin a x \rd x = - \frac {\cos a x} a + C$

where $C$ is an arbitrary constant.

## Proof

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

$\blacksquare$