Chapter 14.7, Problem 13E

Stokes’ Theorem for evaluating line integrals Evaluate the line integral ${\displaystyle {\oint }_{C}F\cdot dr}$ by evaluating the surface integral in Stokes’ Theorem with an appropriate choice of S. Assume that C has a counterclockwise orientation.

13.    F = 〈x² – z², y, 2xz〉; C is the boundary of the plane z = 4 – x – y in the first octant.