16 evaluate jj.f.ds, where f= zî +xi-3y zk and s is the surface of the cylinder x * y = included in the first octant between z = 0 and z = 5 a unit vector norma

16 Evaluate JJ.F.ds, where F= zî +xi-3y zk and s is the surface of the cylinder X * y = included in the first octant between z = 0 and z = 5 A unit vector normal to the surface S(x + yi = 16) is Ex. Sol. 2xi+2yj _xi +yi 4x4y) 4 We have JIFids-lL Fh dx dz where R is the projection of S on the x-z plane. It should be noted that in this case we cannot take the projection of S on the x-y plane as the surface S is perpendicular to the x-y plane.