2 2. (20 points) Verify Gauss' Theorem Fav = [[F.ds for the vector field F = (xz,yz, z²) and V 8V the volume above the paraboloid P: z = x² + y² for z ≤ 4 and below the disk D: x²+y2 <4 with z = 4. Be sure to check and explain the orientations. Use the following steps. a. Compute the divergence . and the volume integral [.Fdv. 7.7 = V 0 y2 X 34 -2 V b. Parametrize the disk, D, and compute the surface integral: Ŕ(7.0) = ē, = ான் Ñ = 武 R(PP) F.N= D (Check the orientation) c. The paraboloid, P, may be parametrize as R(7.0) = (rcose,rsinė, r²). Compute the surface integral: = fo Ñ = 12 R(19) = F.N= [ = F.ds= F.ds to get .ds. d. Combine .ds and JJF.ds D P 8V SSF.ds= 8V (Check the orientation)