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Prove that underset(-a)overset(a)int f(x...

Prove that `underset(-a)overset(a)int f(x)dx={{:(,2underset(0)overset(a)int f(x)dx,"if f(x) is an even function"),(,0,"if f(x) is an odd function"):}` and hence evaluate `underset(-pi//2)overset(pi//2)int (x^(3)+x cos x)dx.`

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