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Math Help - a mixed integration and trig problem

  1. #1
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    a mixed integration and trig problem

    I am working on this question, using all sorts of trig identities, but I didn't get very far. I am not sure also how to do the double integral. The problem is:
    what is given is:

    1. L_{s}=\displaystyle{\int} dxdyD_{s}(x,y)Acos(Kxcos(\Theta)+Kysin(\Theta)-\Phi)
    2. D_{s}(x,y)=\frac{1}{2\pi\sigma_{x}\sigma_{y}}e^{(-\frac{x^2}{2\sigma_{x}^2}-\frac{y^2}{2\sigma_{y}^2})}cos(kx-\phi)

    3. \sigma_{x}=\sigma_{y}=\sigma
    what you have to proove is:

    L_{s}=\frac{A}{2}e^{(-\frac{\sigma^2(k^2+K^2)}{2})}\displaystyle{(}cos(\  phi-\Phi)e^{(\sigma^2kKcos(\Theta))}+cos(\phi+\Phi)e^{  (-\sigma^2kKcos(\Theta))}\displaystyle{)}

    Any help will be greatly appreciated...
    Thanks,
    eran
    Last edited by eldar_e; July 20th 2007 at 11:20 AM.
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  2. #2
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    Changed question into LaTex

    Maybe now it will be easier to solve it..
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