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Math Help - Double Improper Intergral

  1. #1
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    Double Improper Intergral

    Evaluate: \int_0^{\infty}\int_0^{\infty}(1 + x^2 + y^2)^{-2} dxdy

    How would I go about evaluating this integral?
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  2. #2
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    Quote Originally Posted by Shananay View Post
    Evaluate: \int_0^{\infty}\int_0^{\infty}(1 + x^2 + y^2)^{-2} dxdy

    How would I go about evaluating this integral?
    Change to polar coordinates

    remember that x^2+y^2=r^2 and dxdy=rdrd\theta

    This should get you started
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  3. #3
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    Quote Originally Posted by TheEmptySet View Post
    Change to polar coordinates

    remember that x^2+y^2=r^2 and dxdy=rdrd\theta

    This should get you started
    Thanks, I didn't think of that.

    I'm having trouble with the limits again though. I think theta is from 0 to pi/2 but isn't r from 0 to infinity?
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  4. #4
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    Quote Originally Posted by Shananay View Post
    Thanks, I didn't think of that.

    I'm having trouble with the limits again though. I think theta is from 0 to pi/2 but isn't r from 0 to infinity?
    Yes they are both correct.
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