Com \(a\) e \(b\) constantes, a integral indefinida é:

\(\Longrightarrow \int a \cdot \sin \big ( {\pi \over b} x \big ) dx = a\int \sin \big ( {\pi \over b} x \big ) dx\)

\(\Longrightarrow \int a \cdot \sin \big ( {\pi \over b} x \big ) dx = a \Big [ - {\cos \big ( {\pi \over b} x \big ) \over \pi/b} \Big ] + c\)

\(\Longrightarrow \fbox {$ \int a \cdot \sin \big ( {\pi \over b} x \big ) dx = -{ab \over \pi} \cos \big ( {\pi \over b} x \big ) +c $} \)

Sendo \(c\) uma constante qualquer.