Answer
$36 \pi$
Work Step by Step
Divergence Theorem: $\iint_S \overrightarrow{F}\cdot d\overrightarrow{S}=\iiint_Ediv \overrightarrow{F}dV $
$div F=\dfrac{\partial a}{\partial x}+\dfrac{\partial b}{\partial y}+\dfrac{\partial c}{\partial z}=\dfrac{\partial (x^2)}{\partial x}+\dfrac{\partial (-y)}{\partial y}+\dfrac{\partial (z)}{\partial z}=2x$
Now, $I=\iint_{y^2+z^2 \leq 9} \int_0^2 (2x) dxdydz$
This implies that
$I=\iint_{y^2+z^2 \leq 9} [x^2]_0^2 dydz=\iint_{y^2+z^2 \leq 9} (4) dydz=4 \times \iint_{y^2+z^2 \leq 9} dy dz=36 \pi$
