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Theorem Let 
be a continuous function defined on 
, and 
be the region bounded by the curve , the lines 
, 
and the x -axis. Then the volume V of the solid generated by revolving the region one complete revolution about the x -axis is given by
.
Remark In parametric form 
, the volume of solid of resolution generated by revolving the region enclosed by the graph, x -axis and from 
to 
about x -axis
.
Theorem Let be a continuous function defined on , and be the region bounded by the curve , the lines , and 
. Then the volume V of the solid generated by revolving the region one complete revolution about the is given by
.
Example Find the volume of the solid generated by revolving one complete revolution of the upper half region of the closed curve
about the line 
, 
.
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