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I Gaussian integral in two dimensions

  1. Nov 14, 2016 #1
    I am trying to evaluate the following integral.

    ##\displaystyle{\int_{-\infty}^{\infty}f(x,y)\ \exp(-(x^{2}+y^{2})/2\alpha)}\ dx\ dy=1##

    How do you do the integral above?
     
    Last edited: Nov 14, 2016
  2. jcsd
  3. Nov 14, 2016 #2

    Ssnow

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    Gold Member

    Hi, it seems evaluated jet ##=1##, depends what is ##f(x,y)## and ##\alpha##? You must to reformulate the question ...
     
  4. Nov 14, 2016 #3

    mathman

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    Science Advisor
    Gold Member

    Convert to polar coordinates. Integration is straightforward.
     
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