(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Evaluate over the x,y plane:

∫∫[itex]e^{-\sqrt{x^{2}+4y^{2}}}[/itex]dxdy

And I know the answer SHOULD be [itex]\pi[/itex]

2. Relevant equations

Polar-->rectangular identities maybe?

x--> rcos, y--> rsinθ, dxdy--> rdrdθ

3. The attempt at a solution

I tried using polar coordinates, but it doesn't simplify to something nice. When I did I got:

∫∫[itex]r*e^{-r*\sqrt{cosθ^{2}+4sinθ^{2}}}[/itex]drdθ

But there isn't an identity that simplifies the exponent into something easier to handle

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# Evaluating a double integral

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