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Math Help - Find c

  1. #1
    Senior Member pankaj's Avatar
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    Find c

    Let f:[0,1]\rightarrow R be a continuous function such that \int_{0}^{1}f(x)dx=0.

    Prove that there exists some c\in(0,1) such that \int_{0}^{c}xf(x)dx=0
    Last edited by pankaj; March 8th 2013 at 04:18 PM.
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  2. #2
    MHF Contributor
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    Re: Find c

    Hey pankaj.

    Can you split the integral up into pieces where f(x) <= 0 and f(x) > 0 and show that some c exists to balance the first integral?
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