Use Green's Theorem to evaluate $o{\displaystyle \underset{C}{\overset{\phantom{}}{}}}$vec$(F)*dvec(r),$ where vec$(F)(x,y)=($:$9xy-3,-5x^2+9$:$)$ and $C$ is the triangle with vertices $(0,0),(3,0),$ and $(3,1)$ oriented counterclockwise.

The integral obtained from from Green's Theorem is

${}_D,dA$

where $D$ is the interior of the triangle.

This evaluates to

$$