Chapter 6.7, Problem 336E

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

336. [T] Use a computer algebraic system (CAS) and Stokes’ theorem to approximate line integral ${\displaystyle {\int }_c\left(ydx+zdy+xdz\right)}$ , when C is the intersection of plane $x+y=2$ and surface $x^2+y^2+z^2=2\left(x+y\right)$ , traversed counterclockwise viewed from the origin.