Use Green's Theorem to evaluate \(\oint_C \vec{F} \cdot d\vec{r}\), where \(\vec{F}(x, y) = (3xy, y^5 - 5)\) and C is the rectangle with vertices \((-6, -2)\), \((3, -2)\), \((3, 5)\), and \((-6, 5)\).
The integral obtained from from Green's Theorem is
\(\iint_D \Box dA\)
where D is the interior of the rectangle.
This evaluates to
\(\Box\)
