Prove that - -a a fx dx- 2- 0 a fx dx- if f is an evenfunction 0 if f is an odd function and hence evaluate - -1 1 sin 7 x -cos 4 x dx

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Prove that $\int_{- a}^{a} f (x) d x = {\begin{matrix} 2 \int_{0}^{a} f (x) d x, i f f i s a n e v e n f u n c t i o n 0 i f f i s a n o d d f u n c t i o n \end{matrix}$ and hence evaluate $\int_{- 1}^{1} {sin}^{7} x . {cos}^{4} x d x$

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