This is the formulation, which is not clear to me entirely.
Let $S$ be the upper unit half-sphere (this probably means the set $\{(x,y,z)|x^2+y^2+z^2=1, z\geq 0\}$) in the right half-plane plane(I need clarification on what this means), oriented outward with the boundary $\gamma:x^2+y^2=1.$ Apply Stokes' theorem on the form $(x+y+z)dx + x^2dy+xyz\ dz$ on the boundary $\gamma,$ of surface $S$.
I have used the Stokes theorem before but in more clear situations. Input very appreciated. Exam coming up in two days, need to get this concept down.
I am to just apply the Stokes theorem on the half-sphere, taking the boundary as just the unit circle. That simple??