Chapter 6.7, Problem 337E

For the following exercises, use Stokes’ theorem to evaluate ${\displaystyle {\iint }_s\left(curlF\cdot N\right)dS}$ for the vector fields and surface.

337. [T] Use a CAS and Stokes’ theorem to approximate line integral ${\displaystyle {\int }_c\left(3ydx+2zdy-5xdz\right)}$ , where C is the intersection of the xy-plane and hemisphere $z=\sqrt{1-x^2-y^2}$ , traversed counterclockwise viewed from the top—that is, from the positive z-axis toward the xy-plane.