Primitive of Sine Function

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

• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: General Rules of Integration: $14.11$