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Math Help - find volume created by rotating area between 2 curves around line

  1. #1
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    find volume created by rotating area between 2 curves around line

    Calculate the volume found by rotating the area between x^3 and \sqrt{x} around y=1. I found the intersections of the two functions to be 0 and 1. I am using the slice method. Thinking of how it is outer circle-inner circle I do A(x)=\pi(x^3)^2-pi(\sqrt{x})^2. Since the line of reflection is at one of the intercepts that means I don't have to do the y intercept minus the function, I think. So then I get the formula \int_0^1 A(x) and that gives me a negative number
    Last edited by superdude; June 24th 2009 at 09:25 PM.
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  2. #2
    MHF Contributor matheagle's Avatar
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    It haven't done one of these in over 10 years.
    It's important to draw AND note which line you're revolving about.

    The formula I believe is \pi\int_0^1 (R^2-r^2)dx.

    And by looking at the picture, each radius is 1-y.

    So R=1-x^3 is the outer radius and the smaller radius is R=1-\sqrt x.

    Hopefully this leads to a postive volume.
    Last edited by matheagle; June 24th 2009 at 10:10 PM.
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