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Math Help - Calculus Problem

  1. #1
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    Calculus Problem

    LEt a and b be positive integers and y = f(x) be a decreasing differentiable function sucha that f(0) = b and f(a) = 0.

    Prove that the integral of 2xy dx from 0 to a equals the integral of x^2 dy from 0 to b.
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  2. #2
    TD!
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    Well, 2xdx = d(x), the notice the symmetry:

    <br />
\int\limits_0^a {2xydx}  = \int\limits_0^b {x^2 dy}  \Leftrightarrow \int\limits_0^a {ydx^2 }  = \int\limits_0^b {x^2 dy} <br />
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