n 2. Show $\int_{0}^{1} \sin (\pi mx) \sin (\pi nx) d x=\left\{\begin{array}{11} & m eg n 111/2 & men\end{array} ight. $ HINT Use the identity $$ \sin (m x) \sin (n x)=\frac{1}{2}[\cos (m-n) x-\cos (min) x] $$ SP SD 323