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.