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

Use Green's Theorem to prove for the case f(x,y) = 1

[tex]\int\int_R dxdy = \int\int_S |\partial(x,y)/\partial(u,v)|dudv[/tex]

EDIT: R is the region in the xy-plane that corresponds to the region S in the uv-plane under the transformation given by x = g(u,v), y = h(u,v), and the expression on the right is the Jacobian.

2. Relevant equations

[tex]A = \oint _C xdy = -\oint _C ydx = 1/2\oint _C xdy - ydx[/tex]

3. The attempt at a solution

My textbook says that the left side of the equation I'm trying to prove is A(R), so I can apply the first part of the equation in 2., but I don't understand what it's talking about because the equation in 2. deals with line integrals, and I'm trying to prove an equation with double integrals.

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# Homework Help: Prove the change of variables formula for double integrals

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