Chapter 5.1, Problem 43E

In the following exercises, use property y. of double integrals and the answer from the preceding exercise to show that the following inequalities are true.

43. $0\le {\displaystyle \underset{R}{\iint }\left(\ln x\right)\left(\ln y\right)dA\le {\left(e-1\right)}^2}$ where $R=\left[1,e\right]\times \left[1,e\right]$