Verify Stokes’s theorem for $F=z^2\mathbf{i}+5x\mathbf{j}$ and $S: 0\le x\le1,\; 0\le y\le1,\; z=1,\,$ where $C$ is the closed curve enclosing the surface $S$.
I know how to compute Stokes Theorem and I think I know how to do the surface integral however I'm really struggling with how to parameterise the line integral. Any hints or help would be greatly appreciated! Thanks!
I think in this case, it is just easier to compute the line integral directly instead of parametrizing it. The curve C is a square. So you can integrate along each line separately.