Chapter 17.7, Problem 21E

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

21. F = $\langle y,z-x,-y\rangle ;$S is the part of the paraboloid z = 2 − x² − 2y² that lies within the cylinder x²+y²=1.