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Integration to find volume generated

  1. Sep 23, 2010 #1
    To find the volume generated by rotating an area bounded by 2 curves f(x) and g(x) around the x-axis
    we use the formula

    Int of lower and upper intersections pi( f(x)^2-g(x)^2 ) dx


    Int of lower and upper intersections pi (f(x)-g(x))^2 dx

    I understand that they are different but i am confused when to use the correct formula.
  2. jcsd
  3. Sep 23, 2010 #2


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    The first formula would be used if 0 ≤ g(x) ≤ f(x) on the interval [a,b] and the region is being revolved about the x axis. The second one doesn't look like it would ever be correct. If you were revolving the same type area around the y axis with a >0 you would use the "shell" formula

    [tex]\int_a^b 2\pi x(f(x) - g(x)) \ dx[/tex]

    and there are similar formulas for rotation about the y axis.
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