A particle starts at the point (-3, 0), moves along the x-axis to (3, 0) and then along the semicircle $\displaystyle y = \sqrt{9 - x^2}$ to the starting point. Use Green's Theorem to find the work done on this particle by the force field $\displaystyle F(x, y) = (24x, 8x^3 + 24xy^2)$.
(Hint: Work done by a force field $\displaystyle F$ along a curve $\displaystyle C$ is given by the line integral $\displaystyle \int_{C} F \cdot dr$.)