Question: Use Green’s theorem to calculate the work \(W=\int\limits_{C}{\mathbf{F}\cdot d\mathbf{r}}\) done when a particle is moved along the helix \(x=\cos t\), \(y=\sin t\), \(z=2t\), from (1, 0, 0) to (1, 0, \(4\pi \) ) against the force \(\mathbf{F}(x,y,z)=-y\mathbf{i}+x\mathbf{j}+z\mathbf{k}\).