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Method of Shells


Let R be a plane region bounded above by a continuous curve y=f(x), below by the x-axis, and on the left and right by x=a and x=b, then the volume of the solid of revolution obtained by rotating R about the y-axis is given by

 V=2piint_a^bxf(x)dx.

See also

Method of Disks, Method of Washers, Solid of Revolution, Volume

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References

Anton, H. "Volumes by Slicing; Disks and Washers." §6.2 in Calculus with Analytic Geometry, 2nd ed. New York: Wiley, pp. 359-367, 1984.

Cite this as:

Weisstein, Eric W. "Method of Shells." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MethodofShells.html

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