A very useful theorem of multivariate vector calculus is the Gauss Divergence

Theorem:

${\displaystyle \underset{V}{\overset{\phantom{}}{}}}$grad$*vec(F)dV={\displaystyle \underset{A}{\overset{\phantom{}}{}}}$vec$(n)*vec(F)dA$

which governs any continuous arbitrary vector field vec$(F)(vec(R),t).$ Using the following

vector field in rectangular coordinates: vec$(F)=$xvec$()+$zvec$()+$yvec$(k),$ show that the Gauss

Divergence Theorem holds over the region bounded by the following planes:

$x=0,x=4,y=0,y=2,z=0,z=6.$