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Error in integration

  1. Feb 2, 2014 #1
    1. The problem statement, all variables and given/known data

    ## \int_0^2 z^2lnzdz ##


    2. The attempt at a solution

    ## u = lnz, dz = zdu, lim_{t→-∞}\int_t^{ln2} ue^udu ##
    ## lim_{t→-∞}ue^u - e^u l^{ln2}_t ##
    ##2(ln2 - 1) - lim_{t→-∞}\frac {t-1}{e^{-t}} ## Using l'Hospital's rule:
    ##2(ln2 - 1)##

    This is incorrect though. Any pointers on where I went wrong? I believe the domain tom -∞ to ln2 has no discontinuities for the newly defined function and don't seem to see any blatant errors...

    All help is welcomed and greatly appreciated!
     
  2. jcsd
  3. Feb 2, 2014 #2
    Looks like an error in substituting. When you solve for dz, when substituting in you should get:

    [itex]\int^{2}_{0}z^{3}lnzdu[/itex], then with [itex]z = e^{u}[/itex], it should become:

    [itex]\int^{ln2}_{-\infty}ue^{3u}du[/itex]
     
  4. Feb 3, 2014 #3
    I would suggest Integration by Parts rather than a substitution.
     
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