Answer
8
Work Step by Step
Volume below the function $f(x, y)=z$ and above the region $R$ is given by
\[
\begin{array}{c}
\iint_{R} f(x, y) d A=V \\
V=\iint_{R} x^{2} d A \\
=\int_{0}^{2} \int_{0}^{3} x^{2} d y d x \\
=\int_{0}^{2}\left[x^{2} y\right]_{0}^{3} d x \\
=\int_{0}^{2} 3 x^{2} d x \\
=\left[x^{3}\right]_{0}^{2}=2^{3}=8
\end{array}
\]
