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Prove that int(-a)^(a)f(x)dx= {(2int(0...

Prove that `int_(-a)^(a)f(x)dx= {(2int_(0)^(a)f(x)dx ,"if f(x) is even function"),(0, "if f(x) is odd function"):}` and hence evaluate `int_(-(pi)/(2))^((pi)/(2))sin^(7)xdx`

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The correct Answer is:
`int_(-(pi)/(2))^((pi)/(2))sin^(7)xdx =0`
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