Let S be the closed surface which is the part of the cone z = 4 - p x 2 + y 2 above the map z = 0 including the bottom disk and oriented outward. Use the divergence theorem of Gauss to calculate the flux of the field F ~ (x, y, z) = x ~ i + 4y ~ j + z ~ k through S.

12. Soit S la surface fermee qui est la partie du cone z = 4 - vx2 + y2 au dessus du plan z = 0 incluant le disque du bas et orientee vers l'exterieur. Utilisez le theoreme de divergence de Gauss pour calculer le flux du champ F(x, y, z) = xi + 4yj + zk a travers S