A vector field vec$(D)={}^2$hat$(a{)}_{}-3$zhat$(a{)}_z$ exists in a region of a cylinder enclosed by $=1$ and $1z4.$ Verify the divergence theorem by evaluating the following:

$($a$)o{\displaystyle \underset{S}{\overset{\phantom{}}{}}}$vec$(D)*dvec(S)$

$($b$){\displaystyle \underset{v}{\overset{\phantom{}}{}}}(gra{d}^{}*vec(D))dv$