Question: Use Green’s Theorem to calculate the work done by the force F in moving a particle around the closed path C:

\[\begin{aligned} & F\,\left( \,x,\ y\, \right)\quad =\quad \left( \,{{e}^{\,x}}\ -\ 3\,y\, \right)\ i\quad +\quad \left( \,{{e}^{\,y}}\ +\ 6\,x\, \right)\,j \\ & \\ & C:\ r\quad =\quad 2\,\cos \,\theta \\ & \\ \end{aligned}\]