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Prove thatint_(-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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ANSWER :`int_(-(pi)/(2))^((pi)/(2))sin^(7)xdx =0`


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