Exercise text Calculate $ \int_\gamma ydx-xdy+z^2dz $ where $ \gamma $ is the closed curve generated by the intersection of $ x^2+y^2=4 $ with $ z=y^2 $.
My solution and question I tried to solve it by doing the line integral and it comes to me $ 4\pi \sqrt2 $, the problem is that with stokes I can not see what is the surface of intersection.