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

Prove that `int_(0)^(a) f(x) dx = int_(0)^(a) f(a - x)dx` and hence evaluate the following:
(e) `int_(0)^(2)xsqrt(2 - x) dx`.

Answer

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Knowledge Check

  • int_(0)^(2)[x^(2)] dx =

    A
    `5-sqrt2-sqrt3`
    B
    `5-sqrt2+sqrt3`
    C
    `5+sqrt2-sqrt3`
    D
    `-5-sqrt2-sqrt3`

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