4. Use the Divergence Theorem to calculate the surface integral $\iint_S \vec{F} \cdot d\vec{S}$ if $\vec{F} = < x^2z, xz^3, y \ln(x+1) >$, S is the surface of the solid region E bounded by the planes x + 2z = 8, y = 6, x = 0 y = 0 and z = 0. (10 points)
To answer calculate the following first.
4.1 div($\vec{F}$) = $\nabla \cdot \vec{F}$ =
$< \frac{\partial}{\partial x}, \frac{\partial}{\partial y}, \frac{\partial}{\partial z} > \cdot < x^2z, xz^3, y \ln(x + 1) > =$
4.2 $\iint_S \vec{F} \cdot d\vec{S} = \iiint_E div(\vec{F}) dV = $