Chapter 6.7, Problem 358E

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

358. [T] Use a CAS and let $F\left(x,y,z\right)=x{y}^{2}i+\left(yz-x\right)j+e^{yxz}k$ . Use Stokes’ theorem to compute the surface integral of curl F over surface S with inward orientation consisting of cube $\left[0,1\right]\times \left[0,1\right]\times \left[0,1\right]$ with the right side missing.