Fonte Tex:

\displaystyle \int_0^{100}\sin\left(\frac{n\pi x}{100}\right)\sin\left(\frac{m\pi x}{100}\right)dx=\begin{cases}0, \hspace{7mm}\text{se}\hspace{5mm} m\neq n; \\ 50, \hspace{5mm}\text{se}\hspace{5mm}m=n.\end{cases}