Chapter 17.7, Problem 23E

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.

23. $\text{F}=\langle y,1,z\rangle$; S is the part of the surface $z=2\sqrt{x}$ that lies within the cone $z=\sqrt{x^2+y^2}$.