Chapter 6.7, Problem 348E

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

348. Use Stokes’ theorem for vector field $F\left(x,y,z\right)=-\frac{3}{2}{y}^{2}i-2xyj+yzk$ , where S is that part of the surface of plane $x+y+z=1$ contained within triangle C with vertices $\left(1,0,0\right)$ , $\left(0,1,0\right)$ , and $\left(0,0,1\right)$ , traversed counterclockwise as viewed from above.