$\backslash$particle moves from $(0,0)$ to $(1,2)$ due to the vector field F $=2$xy$,$ x$2.$

$($a$)$ Han looks at the path from $(0,0)$ along the axis to $(0,2),$ then from there along a straight

line to $(1,2).$ How much work does the field do$,$ moving the particle along Han$$s path?

$($b$)$ Luke looks at the path along the curve y $=2$x$2.$ How much work does the field do along

this path?

$($c$)$ Leia says they are both nerfherders; it doesn$$t matter what path the particle takes.

What did she notice?

$($d$)$ Find the curl of F to verify Leia$$s intuition.

$($e$)$ Yoda tells them,$$Integrals you need not. Use the potential, you should.$$ Find the

potential function of which he speaks and use it to compute the value of the integrals