Chapter 15.8, Problem 23ES

Let $\sigma$ be the portion of the paraboloid $z=1-x^2-y^2$ for which $z\ge 0,$ and let C be the circle $x^2+y^2=1$ that forms the boundary of $\sigma$ in the xy-plane. Assuming that $\sigma$ is oriented up, use a CAS to verify Formula (2) in stokes’ Theorem for the vector field

$\text{F}=(x^{2}y-z^2){\text{i+(y}}^3-x)\text{j+(2}x+3z-1)\text{k}$

by evaluating the line integral and the surface integral.