in all cases below marks will only be awarded for exact answers n12036

Question

In all cases below marks will only be awarded for exact answers. No marks will be awarded for decimal approximations. Let T be the cylinder x? + y? < 16, 0 <z<1, and let S be thesurface bounding T. Let v be the vector field \mathbf{v}=\left(5 x y^{2} z+y^{2},-3 x^{2} y+z, 3 x^{2} z+6 y\right) Given that \iint_{S} \mathbf{v} \cdot \mathrm{d} \mathbf{S}=A \pi use the divergence theorem to evaluate the integral. State the valueof A.
p. Let be the curved part of the surface S (that is, the surface defined by a2 + y2 = 16, 0 < z < 1). By subtracting the contribution of the flat ends from the previousanswer, or otherwise, evaluate the following integral. \iint_{\Sigma} \mathbf{v} \cdot \mathrm{d} \mathbf{S}=B \pi state the value of B.