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Homework Help: Integral of xln(x) with 0 as a limit of integration

  1. Oct 30, 2011 #1
    1. The problem statement, all variables and given/known data
    Not exactly a homework problem, but I noticed that wolfram alpha gives
    I was wondering why this is so.

    2. Relevant equations & solution attempt
    For [itex]\epsilon>0[/itex]
    Taking [itex]\epsilon \to 0[/itex] gives the answer provided by wolfram alpha.

    My question is what justifies this last step of taking [itex]\epsilon \to 0[/itex]? Continuity?
  2. jcsd
  3. Oct 30, 2011 #2


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    Science Advisor
    Homework Helper

    It's the definition of an indefinite integral with a singularity at one end of the interval of integration.
  4. Oct 30, 2011 #3
    Thank you for your help.
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