Verify that the Divergence Theorem is true for the vector field F = (x², y, z) and the region E the solid cylinder 2+2 <1,0≤≤2 To verify the Divergence Theorem we will compute the expression on each side. First compute di div F dV div F= 2x where div F dV = div F dV = Now compute F F.dS 12 C32 91 1 J₁ = 0 12=2 2x dz dy dx 31=-1 3/2 = 1 21-sqrt(1-y^2) 22 = sqrt(1-y^2) Consider S = DT UDB UCS where Dr is the disk on top (x = 2), DB is the disk on bottom (x = 0) and C's is the cylindrical side. F.dDT = 32 2 dz dy 1 DT 132 2 F.dDB= DB where Cs can be parametrized by r(s, t) = F-dCs -2T = 70 Dr Ds fles F.dDT= F.dDB= F.dCs= Y₁ = Y2= dz dy ds dt 21= 22 S 1 cos(t) with 0 ≤2 and 0 ≤t≤2.