1) , where C is the circle in an anticlockwise direction.

I got 0. Is that right? (Since .)

2) Now this one I'm sort of stuck on:EDIT: Oops! Corrected sign.

where C is closed curve in an anticlockwise direction.

So that equals:

where D is the region bounded by C (the ellipse with radii 2 and 1).

Now the problem here is computation. I opted to go to polar coords (maybe that was a bad idea?), so I got:

. So far so good?

So then I did:

Now.. do I really have to integrate that? Or is there a simpler way?