Hi,

I would like to ask if someone could help me find a solution to this problem.

where C is the ellipse 4x ^ 2 + y ^ 2 = 4 passing through counterclockwise.

What I know so far:

My question:

What are my intervals?

I see that I have a circle in the u and v world, but how do I calculate this double integral in the end? Much appreciated for your time and future effort. Regards

My thoughts right now, I was thinking you could turn from u and v world to r and theta by applying substitution again to polar coordinates for respect to u and v. u^2+v^2=1 is a perfect circle, and then my intervals should be 0< r < 1 and 0 < theta < 2pi. Can that be right?