Let C be the ellipse contained in the xy plane whose equation is \(\displaystyle{4}{x}^{{2}}+{y}^{{2}}={4}\), oriented clockwise. The force field F described by \(\displaystyle{F}{\left({x},{y},{z}\right)}={x}^{{2}}{i}+{2}{x}{j}+{z}^{{2}}{k}\), moves a particle along C in the same direction as the curve orientation, performing a W job. C as the surface boundary S: \(\displaystyle{z}={4}-{4}{x}^{{2}}-{y}^{{2}},{z}\ge{0}\) (with ascending orientation, that is, the component in the z direction equal to 1) and assuming \(\displaystyle\pi={3.14}\), we can state what:

a) It is not necessary to apply Stokes' Theorem, as C is a closed curve and therefore \(W = 0\).

b) Inverting the orientation of the surface S, we can apply Stokes' Theorem and conclude that \(W = 12.56.\)

c) We can apply Stokes' Theorem and conclude that \(W = 6.28\)

d) We can apply Stokes' Theorem and conclude that \(W = 12.56.\)