Chapter 17.7, Problem 14E

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.

14.    F = 〈x² – y², z² – x², y² – z²〉; C is the boundary of the square |x| ≤ 1, |y| ≤ 1 in the plane z = 0.