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Finding Whether Improper Integrals Converge

  1. Oct 17, 2012 #1
    Hi all,

    I'm having trouble with finding an improper integral.

    The problem is ∫10(xln(x))dx

    My book says the answer is -1/4, but I do not understand how this is the case.

    lim(xlnx) as x approaches 1- = 0

    lim(xlnx) as x approaches 0+ = ∞

    So how does this value converge at -1/4?

    Thanks in advance!
     
  2. jcsd
  3. Oct 17, 2012 #2

    pwsnafu

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    Science Advisor

    What makes you say that? Did you try Lhopital?
     
  4. Oct 17, 2012 #3
    Ah. I see that. So now I just find the integral and from zero to one, correct?
     
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