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

Evaluate. ∫∫_{D}x^{2}dA_{xy}, bounded by 5x^{2}+ 4xy + y^{2}= 1

2. Relevant equations

∫∫_{D}H(x,y) dA_{xy}= ∫∫_{D}H(u,v)[itex]\frac{\delta(x,y)}{\delta(u,v)}[/itex]dA_{uv}

3. The attempt at a solution

So I understand I'm supposed to find a change of variables to transform the ellipse into a circle in the uv-plane, and then transform the circle into a square in polar coordinates, which has clearly defined boundaries.

I have no problem taking the integral or making a change of variables, but I'm not sure what to pick for my uv-plane. Clearly, I want to end up with u^{2}+ v^{2}= 1, but how do I figure out what to define my uv-plane as? The part that's throwing me off is the 4xy term.

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# Double integral over a region bounded by an ellipse

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