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Improper Integral Problem (I just want to check my answer)

  1. Oct 20, 2008 #1
    1. The problem statement, all variables and given/known data

    integral (from 0 to 1) of (lnx)dx/(x^0.5)

    2. Relevant equations
    I did u-substitution and got the antiderivative to be 4ln(sqrt(x)) - 4sqrt(x)

    3. The attempt at a solution

    The answer that I got was that the limit of the antiderivative (as t approaches 0 from the right; bounds are 1, t) was infinity, so the integral is divergent.

    I just want to check my answer and see if it is correct. (I have an exam today)
  2. jcsd
  3. Oct 21, 2008 #2


    Staff: Mentor

    Nope. Your antiderivative is wrong. It should be 4sqrt(x)*ln(sqrt(x)) - 4sqrt(x). And the value of the integral (taking the lower limit as t --> 0+) is -4.
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