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Math Help - Volumes

  1. #1
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    Volumes

    The region R is bounded by y=sqrt[x] and y=sqrt[x(x-1)]

    Find the volume by rotating around the x axis.

    I used V=the integral from 0 to 1 of pi[R^2-r^2] which gave me an answer of 2pi/3 which is wrong. The answer is 7pi/6. Am I doing something wrong or do I have to use a different method?
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  2. #2
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    break into two integral expressions ... one using disks, the other using washers

    V = \pi \int_0^1 (\sqrt{x})^2 \, dx + \pi \int_1^2 (\sqrt{x})^2 - \left[\sqrt{x(x-1)}\right]^2 \, dx
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