Chapter 6.7, Problem 356E

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

356. Use Stokes’ theorem to evaluate ${\displaystyle {\iint }_{s}curlF\cdot dS}$ where $F\left(x,y,z\right)=-y^{2}i+xj+z^{2}k$ and S is the part of plane $x+y+z=1$ in the positive octant and oriented counterclockwise $x\ge 0$ , $y\ge 0$ , $z\ge 0$ .