Answer
\[\int_{0}^{2}{\int_{3{{x}^{2}}}^{-6x+24}f(x,y) {dy}dx}\]
Work Step by Step
\[\begin{align}
& \text{Let the region} \\
& R=\left\{ \left( x,y \right):0\le x\le 2,\text{ }3{{x}^{2}}\le y\le -6x+24 \right\} \\
& \text{Then,} \\
& \int_{0}^{2}{\int_{3{{x}^{2}}}^{-6x+24}f(x,y) {dy}dx} \\
& \text{Graph} \\
\end{align}\]
