I'm having trouble verifying Stokes' theorem given a vector field $F(x,y,z)=(y,z,x)$ and the surface $S$, where $S$ is the upper half of the torus generated by rotating the circle $(x-b)^2+z^2=a^2$ about the $z$-axis. I think I've pretty much got the parametrization of $S$, but I don't know what to use for my bounds for that side of Stokes' theorem. Further, on the other side, with the line integral, I have no idea what $C$ should be... any help would be greatly appreciated!
2026-03-26 14:42:22.1774536142
Verifying Stokes' Theorem on upper half of torus
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