Answer
$\dfrac{9}{2}$
Work Step by Step
Divergence Theorem: $\iint_S \overrightarrow{F}\cdot d\overrightarrow{S}=\iiint_Ediv \overrightarrow{F}dV $
Consider $I=\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 $
and $I=\int_0^1\int_0^1 [3x(1)+3(1)-0] dy dx=\int_0^1\int_0^1 (3x+3) dy dx $
Also, $I=\int_0^1 (3x+3)dx =[\dfrac{3x^2}{2}+3x]_0^1$
Hence, $I=\dfrac{3(1)^2}{2}+3(1)=\dfrac{9}{2}$
