## Circulation of F

I know how to do this problem using Stoke's theorem, but my teacher wants me to be able to do it both ways; Stoke's Theorem and line integrals. Thanks for your time!!!

Let F = {y^2, z^2, x} and S be the surface given by the parameterization r(u, v) = {u cos v, u sin v, 4 - u^2} for 0 < u < 2, 0 < v 2pi. Set up an integral that will give the circulation of F along the boundary of S.