Use Stokes' Theorem to evaluate ∫cF ⋅ dr, where F(x, y, z) = x2zi + xy2j + z2k and C is the curve of the intersection of the plane x + y + z = 1 and the cylinder x2 + y2 = 9 oriented counterclockwise as viewed from above.
∫cF ⋅ dr = ∫s curlF ⋅ ds
The Attempt at a Solution
For this problem I am extremely confused of which variant of Stoke's theorem to use and when it is appropriate to use a certain variant. For this problem my teacher found the curlF and then dotted it with the ds. However there are problems in the same section where he uses the left side of Stoke's Theorem. Is it possible to use both? If so, would it be possible to say which would be more advantageous over the other?