Primitive of Sine Function

Theorem

$\ds \int \sin x \rd x = -\cos x + C$

where $C$ is an arbitrary constant.

Corollary

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

Proof

$\map {\dfrac \d {\d x} } {-\cos x} = \sin x$

The result follows from the definition of primitive.

$\blacksquare$