Chapter 17.7, Problem 24E

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.

24. $\text{F}=\langle e^x,1/z,y\rangle$; S is the part of the surface z = 4 − 3y² that lies within the paraboloid z = x² + y².