Chapter 6.7, Problem 330E

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.

330. $\text{F}(x,y,z)=(x+2z)\text{i}+(y-x)\text{j}+(z-y)\text{k}$ ; $S$ is a triangular region with vertices $(3,0,0)$ , $(0,3/2,0)$ , and $(0,0,3)$ .