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Math Help - Integral Proof

  1. #1
    Junior Member ReneG's Avatar
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    Integral Proof

    I need some help getting started.

    If a and b are both positive numbers

    how can I show that \int_0^1 x^a (1-x)^b \,dx = \int_0^1 x^b (1-x)^a\,dx
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  2. #2
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    Re: Integral Proof

    use this property


    \int_a^b {f(x)dx} \\

    a + b - x = y\\

    dx =  - dy\\

    \int_a^b {f(x)dx}  =  - \int_b^a {f(a + b - y)dy = \int_a^b {f(a + b - x)dx} } \\
    Thanks from ReneG
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  3. #3
    Junior Member ReneG's Avatar
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    Re: Integral Proof

    That was much easier than I thought, thank you.
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