5. Find the flux through S. a. Let E = be electro static field. Use the Gauss' Law (JS, E . N dS ) to find the total charge enclosed by the closed surface consisting of the hemisphere z = v1 -x2 - y2 and its circular base in the xy-plane. (Evaluate using N ds = VG dA) b. S: The portion of paraboloid z = g(x, y) = 4-x2 - y? lying above xy-plane, Oriented by upward unit normal vector. F(x, y, z) = . Sketch S first and evaluate. 6. Use the Stokes' thm to evaluate the line integral S F . dr a. Let C is the oriented triangle lying in the plane 2x + 2y + z = 6. where F (x, y, z) = . b. F(x, y, z) = (- y + z) i+ (x-z) j + (x- y) k, S:z= 9 - x2 - y? , z20 7. Use the Divergence thm to evaluate the surface integral F .N dS F(x,y,z) =2xi-2yj+z k and let S be the cylinder x' + y? =4, 0Sz4. Sketch S and evaluate