14. For the vector field F~ (x, y, z) = (x^3 y^2)~i + (y^3 +x)~j + (z^3 + x)~k, calculate the divergence of F~ , i.e. calculate F~ . Then, use the divergence theorem (Gauss) to calculate the surface integral (flux) Z Z S F~ dS~, where S is the oriented surface below which consists of two parts: the hemisphere

14. Pour le champ vectoriel F(x, y, z) = (x3 - y?) i + (y3 + x) j + (23 + x) k, calculer la divergence de F, i.e. calculer V . F. Puis, utiliser le theoreme de divergence (Gauss) pour calculer l'integrale de surface (flux) / / F . dS, ou S est la surface orientee ci-dessous et qui consiste en deux parties: l'hemisphere z = -V1 - x2 - y?, et le disque 0