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

Prove that `int_(0)^(a) f(x)dx=int_(0)^(a) f(a-x)dx` and hence evaluate `underset(0)overset(pi/2)int (cos^(5)x)/(sin^(5)+x+cos^(5)x)dx`.

Answer

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Knowledge Check

  • underset(0)overset(pi)int (cos^(4)x)/(cos^(4)x + sin^(4)x) dx=

    A
    `(pi)/(4)`
    B
    `(pi)/(2)`
    C
    `(pi)/(8)`
    D
    `pi`

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