Chapter 14.7, Problem 15E

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.

15.    F = 〈y², –z², x〉; C is the circle r(t) = 〈3 cos t, 4 cos t, 5 sin t〉, for 0 ≤ t ≤ 2p.