Chapter 16.8, Problem 12E

(a) Use Stokes’ Theorem to evaluate ${\displaystyle {\int }_{c}F\cdot dr},$ where $F\left(x,y,z\right)=x^{2}yi+\frac{1}{3}{x}^{3}j+xyk$ and $C$ is the curve of intersection of the hyperbolic paraboloid $z=y^2-x^2$ and the cylinder $x^2+y^2=1$, oriented counterclockwise as viewed from above.

(b) Graph both the hyperbolic paraboloid and the cylinder with domains chosen so that you can see the curve $C$ and the surface that you used in part (a).

(c) Find parametric equations for $C$ and use them to graph $C$.