Method of Washers
Let f and g be nonnegative and continuous functions on the closed interval [a,b], then the solid of revolution obtained by rotating the curves f(x) and g(x) about the x-axis from x=a to x=b and taking the region enclosed between them has volume given by
![画像: V=piint_a^b{[f(x)]^2-[g(x)]^2}dx.](/index.cgi/contrast/https://mathworld.wolfram.com/images/equations/MethodofWashers/NumberedEquation1.svg){kind=link}
See also
Method of Disks, Method of Shells, Solid of Revolution, VolumeExplore with Wolfram|Alpha
WolframAlpha
References
Anton, H. "Volumes by Cylindrical Shells." §6.3 in Calculus with Analytic Geometry, 2nd ed. New York: Wiley, pp. 367-373, 1984.Referenced on Wolfram|Alpha
Method of WashersCite this as:
Weisstein, Eric W. "Method of Washers." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/MethodofWashers.html