Chapter 8, Problem 48RE

To determine

To find : the volume of the solid.

Answer to Problem 48RE

The volume of the solid is $9.7717$ .

Explanation of Solution

Given information : The bell shaped region bounded by the curves about the y-axis.

Calculation :

From the cylindrical shell method:

  $V={\displaystyle \underset{a}{\overset{b}{\int }}2\pi xf\left(x\right)dx}$

With $f\left(x\right)$ the function that bounds the region is bounded.

  $\begin{array}{l}V={\displaystyle \underset{0}{\overset{1.8933}{\int }}2\pi x\left(3^{1-x^2}-\frac{x^2-3}{10}\right)}dx\\ V=9.7717\end{array}$