Chapter 14.7, Problem 9E

Verifying Stokes’ Theorem Verify that the line integral and the surface integral of Stokes’ Theorem are equal for the following vector fields, surfaces S. and closed curves C. Assume that C has counterclockwise orientation and S has a consistent orientation.

9.    F = 〈y – z, z – x, x – y〉; S is the cap of the sphere x² + y² + z² = 16 above the plane $z=\sqrt{7}$ and C is the boundary of S.