Chapter 17.7, Problem 11E

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.

11.    F = 〈2y, –z, x〉; C is the circle x² + y² = 12 in the plane z = 0.