Chapter 17.7, Problem 5E

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.

5.    F = 〈y, – x, 10〉; S is the upper half of the sphere x² + y² + z² = 1 and C is the circle x² + y² = 1 in the xy-plane.