A Particle Starts at the Point $( - 3,0 )$ , Moves Along the X-Axis to (3, 0) and Then

Multiple Choice

A particle starts at the point $( - 3,0 )$ , moves along the x-axis to (3, 0) and then along the semicircle $y = \sqrt { 9 - x ^ { 2 } }$ to the starting point. Use Green's Theorem to find the work done on this particle by the force field $\mathbf { F } ( x , y ) = \left\langle 24 x , 8 x ^ { 3 } + 24 x y ^ { 2 } \right\rangle$

A) $486$
B) $48 \pi$
C) 0
D) $486 \pi$
E) $972 \pi$