Primitive of Sine Function

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Theorem

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

where $C$ is an arbitrary constant.


Corollary

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


Proof

From Derivative of Cosine Function:

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

The result follows from the definition of primitive.

$\blacksquare$


Sources