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
From Derivative of Cosine Function:
- $\map {\dfrac \d {\d x} } {-\cos x} = \sin x$
The result follows from the definition of primitive.
$\blacksquare$
Also see
Sources
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