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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:
(b) `int_(0)^(pi/2) cos^(2) xdx`.

Answer

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Knowledge Check

  • int_(0)^(pi//2)x sin^2 x dx=

    A
    `pi^2/4 + 1/16`
    B
    `pi^2/16 + 1/4`
    C
    `pi^2`
    D
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  • int_0^(pi) cos^(3) x dx=

    A
    minus 1
    B
    0
    C
    1
    D
    `1/2sqrt2`

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