## Stoke's theorem

S1: $x^2+y^2=1, 1 \leq z \leq 3$
S2: $z=4-x^2-y^2, 3 \leq z \leq 4$
Let $\vec{F}=-yz^3i+2xj-3y^2x^5k$. Evaluate $\int \int (\nabla \times F) \cdot dS$ using
For part (a),I parametrized line which is the circle, then put in vector field F and then dotted with velocity vector, and integrate t from 0 to $2\pi$, but I don't know what happened, I always end up 0!