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How do I calculate the volume of a solid revolution when the axis of revolution is NOT the x or y axis? I thought you do \begin{equation} π∫_a^b f^2(x-c) - g^2(x-c) dx \end{equation} where y=c (a horizontal line) is the axis of revolution, but it doesn't always work. It seems like sometimes I'm supposed to do (c-x) instead, but I can't figure out why. Can anyone explain this to me?

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    I am guessing that you are trying to revolve around $y=c$? If this is the case, you need to shift $f,g$ instead, with appropriate reality checks?2012-05-02

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I am guessing you want $\pi \int_a^b (f(x)-c)^2 - (g(x)-c)^2 \; dx$ instead? (You need, presumably, to check that $f(x)\geq c$, and $g(x)\geq c$ for $x \in [a,b]$.)