Answer
\[\int_{0}^{\ln 10}{\int_{{{e}^{x}}}^{10}{f\left( x,y \right)}dydx}\]
Work Step by Step
\[\begin{align}
& \int_{1}^{10}{\int_{0}^{\ln y}{f\left( x,y \right)}dxdy} \\
& \text{Using the graph to switch the order of integration} \\
& {{e}^{x}}\le y\le 10 \\
& 0\le x\le \ln 10 \\
& \text{Then} \\
& \int_{0}^{\ln 10}{\int_{{{e}^{x}}}^{10}{f\left( x,y \right)}dydx} \\
\end{align}\]
