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Homework Help: Crazy double integral

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

    We want to evaluate the improper integral
    http://ada.math.uga.edu/webwork2_files/tmp/equations/6c/4073055a5b909be16e2abc5bd3dfc61.png [Broken]

    Do it by rewriting the numerator of the integrand as http://ada.math.uga.edu/webwork2_files/tmp/equations/cf/4f71fa0eec36e407d3cf7df46ef3621.png [Broken] 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
    tan^-1(pi*x)?

    Thanks a lot.
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Oct 23, 2006 #2

    quasar987

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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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