Chapter 14.7, Problem 7E

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.

7.    F = 〈x, y, z〉 ; S is the paraboloid z = 8 – x² – y², for 0 ≤ z ≤ 8, and C is the circle x² + y² = 8 in the xy-plane.