Consider the force F~ $=$ a$($xy$2$x $+$ x$2$yy$),$ where a is constant.$($a$)$ Show that F~ is conservative by evaluating its curl.$($b$)$ Evaluate the work done by this force along a path from $($x$,$ y$)=(0,0)$ to $($x$0,$ y$0)$ for the path alongthe x axis from $(0,0)$ to $($x$0,0)$ and then parallel to the y axis from $($x$0,0)$ to $($x$0,$ y$0).$ Use thisresult to write the potential energy function U$($x$,$ y$)$ associated with F~ $,$ assuming U$(0,0)=0$