Suppose

vec$($F$)($x$,$y$)=9$sin$($x$2)$sin$($y$2)$vec$($i$)-9$cos$($x$2)$cos$($y$2)$vec$($j$)$

and C$$is $$the curve from P$$to$$Q$$in $$the figure. Calculate the line integral of $$vec$($F$)$along the curve C$.$

The labeled points are P$=(-3$$2,3$$2),$Q$=(-3$$2,-3$$2),$R$=(3$$2,3$$2),$and S$=(3$$2,-3$$2).$The curves PR $$and SQ $$are trigonometric functions

of $$period $2$ $$and amplitude $1.$

$$Cvec$($F$)*$dvec$($r$)=$