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Math Help - improper integral

  1. #1
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    improper integral

    The question:
    Determine if integral converges or diverges. If converges, evaluate.
    int (xlnx)dx on from 0 to 1.

    It isn't continuous on 0 or 1, right? ln(1)=0. How do I evaluate it when it is not continuous on both sides? Can I just choose 0 or 1 and set it up as a limit and set "b" equal to the other?
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  2. #2
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    Quote Originally Posted by jlmills5 View Post
    The question:
    Determine if integral converges or diverges. If converges, evaluate.
    int (xlnx)dx on from 0 to 1.

    It isn't continuous on 0 or 1, right? ln(1)=0. How do I evaluate it when it is not continuous on both sides? Can I just choose 0 or 1 and set it up as a limit and set "b" equal to the other?
    It's continuous on (0, 1] (try graphing it). You need to evaluate \lim_{b\to 0}\int_b^1 x\ln (x) \mathrm dx.
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