CK12 Calculus - Single Variable

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: