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Volumes by Cylindrical Shells (Calculus II)


Active member
Sep 13, 2013
Quick question, may seem rather dumb - but I just want to make sure of something..

Question: Find the volume of the solid obtained by rotating about the y axis the region between y = x and y = x^2

so when I am setting up my integral am I correct in saying \(\displaystyle TOP - BOTTOM i.e. --> \int^1_0 (2\pi x) (x - x^2) dx\)?


Indicium Physicus
Staff member
Jan 26, 2012
Re: Volumes by Cyllindrical Shells (Calculus II)

It looks good to me. The $2\pi x$ gives you the length of a shell, were you to straighten it out. The $x-x^{2}$ gives you the height of a shell, and the $dx$ gives you the thickness.