Chapter 14.7, Problem 20E

Stokes’ Theorem for evaluating surface integrals Evaluate the line integral in Stakes’ Theorem to determine the value of the surface integral ${\displaystyle {\iint }_S\left(\nabla \times F\right)\cdot ndS}$. Assume that n points in an upward direction.

20.    F = 〈x + y, y + z, z + x〉; S is the titled disk enclosed by r(t) = 〈cos t, 2 sin t, $\sqrt{3}\cos t$〉.