Question: Use Green’s Theorem to calculate the work

done in moving a particle along the semicircle \({{x}^{2}}+{{y}^{2}}=4\), \(y\ge 0\), from \(\left( -2,0 \right)\), \(\left( 2,0 \right)\), against a force \(F\left( x,y \right)={{x}^{2}}\mathbf{i}-y\mathbf{j}\).