Volume of Revolution: About the x-axis
If the animation does not appear, click
here.
This animation shows how revolving a plane region about the x-axis generates a volume.
(See notes below.)
The
volume of revolution that results when the region bounded by the
x-axis, the line x = 0, the line x = 2π, and the curve y = 2 + sin x is revolved about
the x-axis. This animation hows how revolution generates the surface is generated and then
how a moving disk of variable size generates the resulting volume. For a treatment of the way
in which the latter idea can be used to set up a definite integral
for the volume, see the essay
The Definite Integral As an Accumulator. (11/18/07)
An earlier version of this animation was part of a
National Curve Bank
deposit that won the 2004 Renie Award.