In my physics class, we are working on problems using Stokes’ Theorem - but unfortunately we didn’t go over a single example Problem and it’s missing from our textbook! Now, when searching the Internet, it seems that you usually solve for the surface integral using parametrization - but is this strictly necessary? Can you use Stokes’ theorem while remaining in Cartesian coordinates?
Specifically, we are looking to apply Stokes’ theorem to a conservative vector field bounded by the shape with vertices at (1,0,0), (0,1,0) and (0,0,2).
Also, is it valid to set up a triple integral of this problem, integrating the function zero? The problem is that when I try to solve it this way, I get that the answer is just zero, which is not the same answer as I got for the path integral. Could someone maybe provide a hint?
Thank you so much in advance!