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If the region
to be revolved is not bordered by the
axis, the section of the solid is not a disk,
but an annulus.
Denote by
the function whose graph is the outer boundary of the region
, and by
the function whose graph
is the inner boundary of
; suppose that both functions are continuous on
, where
.
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We revolve about the
axis the region bounded by the parabolas whose respective equations are
and
, by the
axis and the line whose equation is
, i.e. the region
in Figure
7.
The volume of the solid is given by:
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Noah Dana-Picard 2007-12-28