सोडोवचें ∫ (from 0 to pi) of cosmxcosnx wrt x

$$\int _ { 0 } ^ { \pi } \cos m x \cos n x d x$$

मूल्यांकन करचें

$$\left\{\begin{matrix}\frac{m\sin(\pi m)\cos(\pi n)-n\sin(\pi n)\cos(\pi m)}{m^{2}-n^{2}},&|m|\neq |n|\\\frac{\sin(2\pi n)+2\pi n}{4n},&n\neq 0\text{ and }|m|=|n|\\\pi ,&n=0\text{ and }m=0\end{matrix}\right.$$

w.r.t. m चो फरक काडचो

$$\left\{\begin{matrix}\frac{-m^{2}\sin(\pi m)\cos(\pi n)-n^{2}\sin(\pi m)\cos(\pi n)+\pi nm^{2}\sin(\pi m)\sin(\pi n)-\pi mn^{2}\cos(\pi m)\cos(\pi n)+\pi m^{3}\cos(\pi m)\cos(\pi n)-\pi n^{3}\sin(\pi m)\sin(\pi n)+2mn\sin(\pi n)\cos(\pi m)}{\left(m^{2}-n^{2}\right)^{2}},&|m|\neq |n|\\0,&|m|=|n|\end{matrix}\right.$$