1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Double integral using the dirac delta

  1. May 21, 2009 #1
    1. The problem statement, all variables and given/known data

    Need to integrate using the dirac delta substitution:
    [tex]
    \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}\!x^2\cos(xy)\sqrt{1-k^2\sin^2(y)}\, dx\, dy
    [/tex]

    2. Relevant equations
    [tex]\cos(xy) = \frac{1}{2}\left(e^{ixy} + e^{-ixy}\right)[/tex]

    [tex]\delta\left[g(t)\right] =
    \frac{1}{2\pi}\int_{-\infty}^{\infty}\!e^{ikg(t)}\,dk[/tex]

    3. The attempt at a solution

    1) First I tried replacing cos with the exponents, this allowed breaking the integral into two (almost identical ;) ) parts.
    2) Next I should use the second formula (the one with delta) and replace exp with delta, which would help me to get rid of the x-parts...

    but the problem is how can I substitute delta when I have something like this (how to deal with the x^2 ???):
    [tex]\frac{1}{2\pi}\int_{-\infty}^{\infty}\!x^2e^{ix(y)}\,dx[/tex]
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Double integral using the dirac delta
Loading...