Chapter 6.7, Problem 338E

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

338. [T] Use a CAS and Stokes’ theorem to approximate line integral ${\displaystyle {\int }_c\left[\left(1+y\right)zdx+\left(1+z\right)xdy+\left(1+x\right)ydz\right]}$ , where C is a triangle with vertices $\left(1,0,0\right)$ , $\left(0,1,0\right)$ , and $\left(0,0,1\right)$ oriented counterclockwise.