Answer
$\dfrac{9}{2}$
Work Step by Step
The Divergence Theorem states that $\iint_S \overrightarrow{F}\cdot d\overrightarrow{S}=\iiint_Ediv \overrightarrow{F}dV $
Here, we have $\iint_S \overrightarrow{F}\cdot d\overrightarrow{S}=\iiint_Ediv \overrightarrow{F}dV =\int_0^1\int_0^1\int_0^1 (3x+3) dz dy dx $
$=\int_0^1\int_0^1 [3xz+3z]_0^1 dy dx $
$=\int_0^1\int_0^1 3x(1)+3(1)-0 dy dx $
$=\int_0^1\int_0^1 (3x+3) dy dx $
$=\int_0^1 (3x+3)dx $
$=[(3/2)x^2+3x]_0^1$
$=\dfrac{9}{2}$