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Thread: strange double integral

  1. March 16th 2009, 06:39 AM #1
    fiksi
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    strange double integral

    Don't have idea what to do with this...

    I(- to + infiniti) I(- to + infiniti) (x2+y2)e to the power of(-x4 -(2x2) * y2 -y4) dy dx

    So it is a double integral...
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  2. March 16th 2009, 03:26 PM #2
    Danny
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    Quote Originally Posted by fiksi View Post
    Don't have idea what to do with this...

    I(- to + infiniti) I(- to + infiniti) (x2+y2)e to the power of(-x4 -(2x2) * y2 -y4) dy dx

    So it is a double integral...
    Switching to polar coords
    \int_{-\infty}^\infty \int_{-\infty}^\infty (x^2+y^2) e^{-x^4-2 x^2 y^2-y^4}\,dx \,dy = \int_0^{2\pi} \int_0^\infty r^3 e^{-r^4}\, dr\, d \theta which I believe is integrable.
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