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How to do this integral ?

  1. May 21, 2014 #1

    I'm stumbled on the following integral,

    [itex]\int d\vec{q} e^{i\vec{q}\vec{r}} \cos(2\theta)[/itex],

    where [itex] \theta[/itex] denotes the angle of the vector [itex] \vec{q} [/itex] and the [itex] \vec{r}[/itex] is an arbitrary vector. The integral domain is a circular area of radius [itex] D [/itex].

    Could anyone help me out ?

    Many thanks.

  2. jcsd
  3. May 21, 2014 #2


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    Science Advisor

    Try cos(2θ) =(exp(2iθ)+exp(-2iθ))/2
  4. May 21, 2014 #3
    Thanks for your response.

    I have worked it out. It amounts to zero by symmetry.
  5. May 24, 2014 #4
  6. May 24, 2014 #5
    If you're going to ignore both the original poster's notation (##\theta## has a specific meaning, and it's a vector integral) and the domain of integration, you can't expect to just type the integral into Wolfram Alpha and expect to get the right result.
  7. May 24, 2014 #6
    I'm sorry for that , I'm not great in calculus and I probably skimmed through the posts.
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