I just posted something with this but now I want to use Green's Theorem:
Compute the following three line integrals directly around the boundary C of the part R of the interior ellipse (x^2/a^2)+(y^2/b^2)=1 where a>0 and b>0 that lies in the first quadrant:
(a) integral(xdy-ydx)= double integral(2)dA what are the bounds?
(b) integral((x^2)dy)= double integral(-2x)dA what are the bounds?
(c) integral((y^2)dx)= double integral(2y)dA what are the bounds?
I know how to evaluate all the double integrals, I just don't know the bounds. I'm assuming I would use parameterization.
I think the answer for (a) is (pi/2)*ab, for (b) is (2/3)*(a^2)b, and for (c) is (-2/3)*a(b^2), but I solved them directly from a line integral not Green's Theorem.