Chapter 8, Problem 25RE

To determine

To find : the volume of the solid.

Answer to Problem 25RE

The volume of the solid is $2\pi -\ln \left(3\right)\pi$ .

Explanation of Solution

Given information : the region enclosed by the graphs of $y=e^{\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$2$}\right.},y=1$ , and $x=\ln 3$ is revolved about the x -axis.

Calculation :

By the washer method to subtract the cylindrical part in the middle of the solid.

The integral which is:

  $\begin{array}{l}{\displaystyle \underset{0}{\overset{\ln 3}{\int }}\pi \left(e^x-1\right)}dx\\ \Rightarrow \pi \left(e^x-x\right)\\ \Rightarrow \pi \left(2-\ln \left(3\right)\right)\\ \Rightarrow 2\pi -\ln \left(3\right)\pi \end{array}$