Chapter 8.3, Problem 65E

To determine

To choose : the correct option.

Answer to Problem 65E

The correct option is (a) $0.718$ .

Explanation of Solution

Given information : The base of a solid $S$ is the region enclosed by the graph of $y=\ln x$ , the line $x=e$ , and the x-axis. If the cross section of $S$ perpendicular to the x-axis are squares.

  $\begin{array}{l}y=\ln x,x=e,y=0\\ V={\displaystyle \underset{1}{\overset{e}{\int }}{S}^{2}xdx}\\ V={\displaystyle \underset{1}{\overset{e}{\int }}{\left(\ln x-0\right)}^{2}dx}\\ V={\displaystyle \underset{1}{\overset{e}{\int }}{\ln }^{2}xdx}\\ V=0.718\end{array}$