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Help with volume of solid of revolution/integration by parts question

  1. Feb 12, 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

    I've set up the integral via disk method: π∫(e^√x)^2 dx from 0 to 1

    I've done integration by parts by don't know how to integrate the second term of the integration by parts which is: ∫(xe^2√x)/(√x) dx from 0 to 1

    Also the answer to the question is (π/2)(e^2+1)
     

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  2. jcsd
  3. Feb 12, 2014 #2

    LCKurtz

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    That problem obviously has a typo in it somewhere. Your integral is correct but it is not an elementary integral and won't match any of the answers.
     
  4. Feb 12, 2014 #3
    I'm pretty sure there's no typo in the question, when I plug in the integral into wolfram alpha, I get the correct answer which is (π/2)(e^2+1)
     
    Last edited: Feb 12, 2014
  5. Feb 12, 2014 #4

    PeroK

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    How did you do the integration by parts? For the integral:

    [tex]\int_0^1 e^{2\sqrt{x}}dx[/tex]

    Did you think about a substitution?
     
  6. Feb 12, 2014 #5

    LCKurtz

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    Yep. I looked at it too quickly. Try ##2\sqrt x = \ln u## on it.
     
  7. Feb 12, 2014 #6

    u=e^(2√x) dv=dx
    du=(e^(2√x))/(√x) dx v=x

    ∫e^(2√x)dx = xe^(2√x) - ∫((xe^(2√x))/(√x)
     
  8. Feb 12, 2014 #7

    PeroK

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    I think parts was the wrong way to go. What about the obvious substitution u = √x? In the original integral.
     
  9. Feb 12, 2014 #8
    I don't think u-substitution works in this case, also the directions specifically ask to solve the question via integration by parts.

    Also here's the original integral:

    π∫e^(2√x) dx, from 0 to 1
     
  10. Feb 12, 2014 #9

    PeroK

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    The u-substitution does work. It simplifies things ready for the integration by parts!
     
  11. Feb 12, 2014 #10

    LCKurtz

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    Substitution does work. Try one of the substitutions that have been suggested and you will see.
     
  12. Feb 12, 2014 #11
    Could you please show exactly how you would do the u-substitution before doing integration by parts? I want to make sure I understand this concept etc.
     
  13. Feb 12, 2014 #12

    PeroK

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