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Math Help - prove using integration by parts

  1. #1
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    prove using integration by parts

    I tried doing this, but ended up at a dead end.

    Use integration by parts to show that the integral from 0 to 1 of f''(x)g(x)dx = the integral from 0 to 1 of f(x)g''(x)dx.

    suppose f(0)=g(0)=0 and f(1)=g(1)=0. give examples for g(x) and f(x).
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  2. #2
    Senior Member
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    Are f(0)=g(0)=f(1)=g(1)=0 suppositions of the first problem?

    With integration by parts, we obtain a new integral by integrating one factor and differentiating the other. It's a way to bump one factor up and the other down, so to speak. For example,

    \int f'(x)g(x)\,dx=f(x)g(x) - \int f(x)g'(x)\,dx.

    The problem given can be solved by integrating f and differentiating g twice.
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