Chapter 14.7, Problem 17E

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.

17.    F = 〈x, y, z〉; S is the upper half of the ellipsoid x²/4 + y²/9 + z² = 1.