Note:The alert readerwill havenoticedthat this examplecouldbe workedwith a simplerintegralusing
disks.However, the followingexamplecan only be solvedwith shells.
Example7:
Find the volumeof the solidgeneratedby revolvingthe regionboundedby ,
and about
Figure 16
Solution:
As you can see, the equation cannotbe easilysolvedfor and thereforeit will be
necessaryto solvethe problemby the shell method.We are revolvingthe regionabouta line parallelto the
-axisand thus integratewith respectto Our formulais
In this case,the radiusis and the heightis. Substituting,