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Improper integral

  1. Feb 9, 2008 #1
    1. The problem statement, all variables and given/known data

    Show that the integral of (1/x)sin(1/x)dx from 0 to 1 is converges absolutely?


    2. Relevant equations



    3. The attempt at a solution

    Should we use the comparison test in this situation?
     
  2. jcsd
  3. Feb 9, 2008 #2

    quasar987

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    Try a change of variables first.
     
  4. Jun 15, 2011 #3
    change of variable u=1/x you will get from 1 to infinite integral of -sinu over u after that you do integration by parts and you will get your answer sinu / u is always convergent
     
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