you're using the 3d equation when you want to use the 2d equation. Remember, N is the unit normal vector pointing perpendicular to the circle, and dont forget to convert to polar coords.
Let F be the vector field F=1/3(x^3)i+1/3(y^3)j , and let S be the unit circle r(t)=(cost)i+(sint)j for 0<t<2pi and let Q be the domain enclosed within the circle.
1) How to show that the tangential form of Green's Theorem is satisfied for the given field, curve and domain.