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A very useful theorem of multivariate vector calculus is the Gauss Divergence Theorem: V grad * v e c ( F ) d V =

A very useful theorem of multivariate vector calculus is the Gauss Divergence
Theorem:
Vgrad*vec(F)dV=Avec(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.
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