Chapter 6.7, Problem 344E

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

344. Use Stokes’ theorem to evaluate line integral ${\displaystyle {\int }_c\left(zdx+xdy+ydz\right)}$ , where C is a triangle with vertices $\left(3,0,0\right)$ , $\left(0,0,2\right)$ , and $\left(0,6,0\right)$ traversed in the given order.