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Help with Volume of Revolution/Trig Substitution Problem

  1. Feb 24, 2014 #1
    1. The problem statement, all variables and given/known data

    The problem is attached in this post.

    2. Relevant equations

    The problem is attached in this post.


    3. The attempt at a solution

    Disk method with the radius equal to x/((x^2+3)^5/4)

    For Trig Substitution √(x^2+a^2) -> x=atanθ
    a=√3 -> a^2=3
    x=√(3)tanθ -> dx=√(3)sec^2(θ)
    x^2=3tan^2(θ)


    Volume=π∫((3tan^2(θ)√(3)sec^2(θ))/(3tan^2(θ)+3)^5/4 from 0 to π/6

    I can't seem to simplify the integral to the point where I can get the answer etc.

    The answer is π/72
     

    Attached Files:

  2. jcsd
  3. Feb 24, 2014 #2

    tiny-tim

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    hi student93! :smile:

    (try using the X2 button just above the Reply box :wink:)

    i haven't checked, it's too difficult to read :redface:, but you seem to have inserted an extra tanθ somewhere …

    π∫((3tan(θ)√(3)sec2(θ))/(3tan2(θ)+3)5/4 can be simplified :smile:
     
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