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Improper integral concept question

  1. Mar 30, 2011 #1
    1. The problem statement, all variables and given/known data

    For what values of K is the following integral improper?

    [tex]\int\stackrel{K}{0}x^2 / (x^2-19x+90) dx[/tex]

    I'm stuck on this question. I understand mechanically, that the integration require partial fraction decomp, which results in -9ln(x-9) (from 0 to K) + 10ln(x-10) (from 0 to K). What I don't understand is what makes this integral improper. I understand that LN is undefined for all evaluations < 1. So does this mean that any K < 10 will create an improper integral?

    EDIT: How does one properly display the upper and lower limits on the integration symbol?
    Last edited: Mar 30, 2011
  2. jcsd
  3. Mar 30, 2011 #2
    To get the limits right use \int_0^K instead of stackrel.

    As for the question itself, you might want to draw a sketch of the function.
  4. Mar 30, 2011 #3


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    Staff Emeritus
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    An integral may be "improper" for one of several reasons-
    1) The lower limit is [itex]-\infty[/itex].
    2) The upper limit is [itex]\infty[/itex].
    3) The integrand goes to [itex]-\infty[/itex] at some point in the interval of integration.
    4) The integrand goes to [itex]\infty[/itex] at some point in the interval of integration.

    Which of those can happen here?

    What values of x make the denominator of the integrand 0?
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