Consider the following.

F$($x$,$ y$)=$

$2$xy

i $$

x$2$y$2$

j

P$(5,5)$ to Q$(9,7)$

$($a$)$

Show that

$$C

$$F $$ dr

is independent of path.

$$N$$x

$=$

$$M$$y

$=$

$($b$)$

Calculate the work done by the force field F on an object moving along a curve from P to Q$.$