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Crazy double integral

  1. Oct 23, 2006 #1
    Here's the question:

    We want to evaluate the improper integral

    Do it by rewriting the numerator of the integrand as [​IMG] for appropriate f, g and h and then reversing the order of integration in the resulting double integral.

    I don't know what this means?

    Would the integrand in the numerator be x from tan ^-1(x) to

    Thanks a lot.
  2. jcsd
  3. Oct 23, 2006 #2


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    It says find the function h(x), f(x) and g(x) such that

    [tex]\tan^{-1}(\pi x) - \tan^{-1}(x) = \int_{f(x)}^{g(x)}h(y)dy[/tex]

    Said like that, and based on your knowledge of the fundamental thm of calculus, it should be very easy to see what h(x), f(x) and g(x) are.
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