Chapter 14.7, Problem 18E

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.

18.    F = r/|r|; S is the paraboloid x = 9 – y² – z² for 0 ≤ x ≤ 9 (excluding its base), where r = 〈x, y, z〉.