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!

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- Mar 15th 2010, 09:41 AMamywilliams99Double 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! - Mar 15th 2010, 10:39 AMtom@ballooncalculus
Sorry, error

- Mar 15th 2010, 11:00 AMamywilliams99
Some one please help!

I have attempted to use x = rcos(theta) and y=rsin(theta) but cant seem to get an answer. - Mar 15th 2010, 12:30 PMshawsend
Hi. How about using polar coordinates? You know $\displaystyle x^2+y^2=r^2$ right? Then turn the crank:

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