I have the following question:
I've managed to do the surface integral part of stokes theorem (and got an answer of 0) however I'm having a lot of trouble doing the line integral part in order to verify the theorem.
As I understand it, I should be doing a line integral around the part of the plane $z = 2-2x-y$ that's in the $x,y,z > 0$ quadrant of the $x$ $y$ and $z$ axes but I don't know how to parametrize that particular part seeing as it's in 3D. All the examples I've done so far have been solely in the $xy$ plane.
Should I treat each side of the path I'm going to traverse as a separate line and then just do all four and add their answers up? Or am I missing something really simple?