Chapter 15, Problem 18RE

Let $\text{F}\left(x,y\right)=\left(y{e}^{xy}-1\right)\text{i}+x{e}^{xy}\text{j}.$

(a) Show that F is a conservative vector field.

(b) Find a potential function for F.

(c) Find the work performed by the force field on a particle that moves along the sawtooth curve represented by the parametric equations $\begin{array}{c}x=t+{\sin }^{-1}\left(\sin t\right)\\ y=\left(2/\pi \right){\sin }^{-1}\left(\sin t\right)\end{array}\begin{array}{c}\left(0\le t\le 8\pi \right)\end{array}$

(see the accompanying figure).