1. ## Vector Analysis

Evaluate

$\displaystyle \int\int_S \left[\frac{1}{R}\nabla{\phi} - \phi\nabla{\left(\frac{1}{R}\right)}\right]\cdot d\bold{S}$

over the surface of the sphere $\displaystyle (x-3)^2 + y^2 + z^2 = 25$, where $\displaystyle \phi = xyz + 5$

2. I see a vector valued function dotted into the normal of a ball centered at (3,0,0). Can't you use the divergence theorem? So instead of evaluating
$\displaystyle \vec f \cdot n dS$
$\displaystyle \nabla \cdot \vec f dV$
$\displaystyle \nabla \cdot \nabla \frac{1}{r}$
$\displaystyle \nabla \cdot \nabla (xyz+5)$