Double Improper Intergral

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June 7th 2010, 12:24 PM
Shananay

Double Improper Intergral

Evaluate: $\int_0^{\infty}\int_0^{\infty}(1 + x^2 + y^2)^{-2} dxdy$

How would I go about evaluating this integral?
June 7th 2010, 12:25 PM
TheEmptySet

Quote:

Originally Posted by Shananay

Evaluate: $\int_0^{\infty}\int_0^{\infty}(1 + x^2 + y^2)^{-2} dxdy$

How would I go about evaluating this integral?

Change to polar coordinates

remember that $x^2+y^2=r^2$ and $dxdy=rdrd\theta$

This should get you started
June 7th 2010, 12:46 PM
Shananay

Quote:

Originally Posted by TheEmptySet

Change to polar coordinates

remember that $x^2+y^2=r^2$ and $dxdy=rdrd\theta$

This should get you started

Thanks, I didn't think of that.

I'm having trouble with the limits again though. I think theta is from 0 to pi/2 but isn't r from 0 to infinity?
June 7th 2010, 01:13 PM
TheEmptySet

Quote:

Originally Posted by Shananay

Thanks, I didn't think of that.

I'm having trouble with the limits again though. I think theta is from 0 to pi/2 but isn't r from 0 to infinity?

Yes they are both correct.

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