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

Show that T(u,v) = (u^{2}- v^{2}, 2uv)

maps to the triangle = {(u,v): 0 ≤ v ≤ u ≤ 4} to the domain D

bounded by x=0, y=0, and y^{2}= 1024 - 64x.

Use T to evaluate ∬_{D}sqrt(x^{2}+y^{2}) dxdy

2. Relevant equations

3. The attempt at a solution

x=u^{2}-v^{2}

y=2uv

Jacobian= 4u^{2}+4v^{2}dudv

I guess the equation in the changed variable integral should be ∫∫sqrt((u^{2}-v^{2})^{2}+(2uv)^{2}) (4u^{2}+4v^{2}) dudv

But, I don't know how to get the bounds for the integrals in terms of u and v.

Can someone help me on this??

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# Help with Changing of variables, Jacobian, Double Integrals?

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