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Homework Help: Volume of a rotating solid

  1. Feb 10, 2013 #1
    1. The problem statement, all variables and given/known data
    Region: f(x) = 2 sin x on the interval [0, π]. Find the volume of
    the 3D solid obtained by rotating this region
    about the dashed line y = −1.

    2. Relevant equations

    Integration of pi∫(2sin(x) + 1)^2 dx

    3. The attempt at a solution

    http://www3.wolframalpha.com/Calculate/MSP/MSP85361a550f47a75i0g7800002h3g026g9d9ieg7f?MSPStoreType=image/gif&s=3&w=301&h=35 [Broken]

    That does not seem to work. I am completely baffled as to what I am doing wrong.
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 10, 2013 #2


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    Science Advisor
    Homework Helper
    Gold Member

    f(x) = 2 sin x on the interval [0, π] does not define a region. It defines a curve and two limits on the x coordinate. You seem to be assuming the remaining boundary is the line y = -1, but why that rather than, say, the x axis?
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