Chapter 6.7, Problem 340E

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

340. [T] Use a CAS and Stokes’ theorem to evaluate ${\displaystyle {\iint }_s\left(curlF\cdot N\right)dS}$ , where $F\left(x,y,z\right)=x^{2}yi+x{y}^{2}j+z^{3}k$ and C is the curve of the intersection of plane $3x+2y+z=6$ and cylinder $x^2+y^2=4$ , oriented clockwise when viewed from above.