I'm currently working on a problem that asks me to verify Stoke's theorem. The issue I'm currently running into is calculating the da.
For Stoke's Theorem, $\int_V (\nabla \times r) \cdot da$, I currently have the value of $(\nabla \times r)$, and I just need to dot product it with each of the surfaces given by the shape below. I am trying to do this in spherical coordinates (and that is what my $(\nabla \times r)$ vector is in), but I can't figure out how one would go about getting the area element for a surface like the back triangle in spherical coordinates.
How are you supposed to approach these issues when there is no obvious way to deduce da?
