- #1
Idoubt
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- 1
Homework Statement
I want to evaluate the following definite integral of the form,
[tex] I = \int\limits_{x = -\infty}^{\infty}\int\limits_{y = -\infty}^{\infty} e^{-ax^2} e^{-by^2} | \cos(c x + d y)| dx dy[/tex]
where a, b, c, and d are constants, as part of a larger problem I am doing,
Homework Equations
[tex] \cos x = \frac{1}{2} ( e^{ix} + e^{-ix}) [/tex]
[tex] \int\limits_{-\infty}^{\infty} e^{-a(x - b)^2} dx= \sqrt{\frac{\pi}{a}}[/tex]
The Attempt at a Solution
If it wasn't for the abs value on the cos function it would be easy to write it in terms of exponentials and complete squares and perform the integral. As it is I don't know how to approach this, any help would be great. I have given a general form of the integral but for my purpose it's ok to assume a =b.