- #1
PinkCrayon
- 9
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Homework Statement
Evaluate. ∫∫D x2 dAxy, bounded by 5x2 + 4xy + y2 = 1
Homework Equations
∫∫D H(x,y) dAxy = ∫∫D H(u,v)[itex]\frac{\delta(x,y)}{\delta(u,v)}[/itex]dAuv
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 u2 + v2 = 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.