Chapter 6.7, Problem 326E

For the following exercises, without using Stokes’ theorem, calculate directly both the flux of curl $\text{F}\cdot \text{N}$ over the given surface and the circulation integral around its boundary, assuming all boundaries are oriented clockwise as viewed from above.

326. $\text{F}(x,y,z)=y^2\text{i}+z^2\text{j}+x^2\text{k}$ ; $S$ is the first-octant portion of plane $x+y+z=1$ .