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Shell method to find volumes: need to find intersections of the curves involved?

  1. Nov 5, 2011 #1
    In the Shell (or cylinder) method in integration to find the volume of a solid created by revolving a figure around an axis fo
    For the figure bounded by y=f(x) , y=g(x), x=a and x=b, rotated around the vertical axis x = s,
    then the resulting volume is the integral from a to b of 〖2π|x-s|∙|f(x)-g(x)|dx〗

    Similarly for rotating around a horizontal axis. The formula is clear, but all the examples I find have either for all x, a≤x≤b → f(x)≤ g(x) or
    for all x, a≤x≤b → f(x)≥ g(x).
    However, I am suspicious as to what happens when neither of these conditions are met. In calculating areas with integrals, one has to break up the region into sections. Does one have to do that for the volumes in this method, or do the absolute values given in the formula suffice?
    Thanks.
     
  2. jcsd
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