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Help with integral problem

  1. Feb 25, 2014 #1
    1. The problem statement, all variables and given/known data

    Question is attached in this post.


    2. Relevant equations

    Question is attached in this post.

    3. The attempt at a solution

    I set the integral as ∫(cos^1/2(x))(1-cos^2(x))(sinx) dx from 0 to π/2

    Next I used u-substitution where I let u=cosx and du=-sinxdx

    I solved out the integral and ended up getting 7/6 as my answer, however the correct answer is 8/21. Was my approach incorrect?
     

    Attached Files:

  2. jcsd
  3. Feb 25, 2014 #2

    PhysicoRaj

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    You might be wrong in applying limits and simplifying. Check it. :)
     
  4. Feb 25, 2014 #3

    SteamKing

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    Obviously, something went wrong, but we can't say unless you show the details of your work.
     
  5. Feb 25, 2014 #4
    Could you please tell me how I used the wrong limits, and what the actual limits are? (This question is really frustrating me and I have an exam in a few hours etc.).
     
  6. Feb 25, 2014 #5

    PhysicoRaj

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    Have you changed the limits according to your substitution?
    The limits given are for x. Calculate them for u.
    OR
    have you replaced u by an x function?
     
  7. Feb 25, 2014 #6
    ∫cosx^1/2(1-cos^2x)sinxdx

    u=cosx
    du=-sinxdx

    -1∫u^1/2 - u

    = -1((u^3/2)(2/3))(u^2/2)

    = -1((cos^3/2(x))(2/3))cos^2(x)/2 -> Upper Limit = π/2 and Lower Limit =0

    My answer comes out to 7/6, is the method that I used even correct? (Or should I have had used another method?)
     
  8. Feb 25, 2014 #7

    PhysicoRaj

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    -1∫u^1/2 - u .....you have this wrong.
     
  9. Feb 25, 2014 #8
    How? I'm just really confused lol, shouldn't the be correct? Did I make a simple mistake?
     
  10. Feb 25, 2014 #9

    PhysicoRaj

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    √u(1-u2)
    =√u-u2+0.5
    =√u-u5/2
     
  11. Feb 25, 2014 #10
    Thanks, I'll try to see if I can get the correct answer now.
     
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