Double Integrals Problem

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March 15th 2010, 09:41 AM
amywilliams99

Double Integrals Problem

I must solve the double integral -
∫ ∫ (x^2 + y^2) e^(-x^4 - 2(x^2)(y^2) - y^4) dy dx
Both integrals between infinity and - infinity!
Please help!
March 15th 2010, 10:39 AM
tom@ballooncalculus

Sorry, error
March 15th 2010, 11:00 AM
amywilliams99

Some one please help!
I have attempted to use x = rcos(theta) and y=rsin(theta) but cant seem to get an answer.
March 15th 2010, 12:30 PM
shawsend

Hi. How about using polar coordinates? You know $x^2+y^2=r^2$ right? Then turn the crank:

$\int_{-\infty}^{\infty}\int_{-\infty}^{\infty} (x^2+y^2)e^{-(x^2+y^2)^2} dydx=\int_0^{2\pi}\int_0^{\infty}r^2 e^{-r^4}rdrdt$

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