Areaof a Surfaceof Revolution
If f is a smoothand non-negativefunctionin the interval then the surfacearea generatedby re-
volvingthe curve between and aboutthe -axisis definedby
Equivalently, if the surfaceis generatedby revolvingthe curveaboutthe -axisbetween and
then
Example1:
Find the surfacearea that is generatedby revolving on aboutthe -axis(Figure21).
Solution: