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?
Axis of revolution
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integration
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0You can always rotate your coordinate system so that the axis of revolution is a coordinate axis... – 2012-05-02
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0@J.M.: I think that SRK's problem is with an axis of the form $x=c$ when $c\ne 0$, not with an oblique axis of revolution. – 2012-05-02
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0SRK, if it is as @Brian describes, then things are easier; you can just shift your axis... – 2012-05-02
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5You seem to be looking for a general formula. It can be given, but understanding logic of a few concrete cases is much more useful. – 2012-05-02
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0I 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