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How to solve an Improper Integral of Type 2?

  1. May 5, 2005 #1
    I've posted on Homeworks one of the number I did not understand. However, I would like to know the steps to calculate an improper integral of type 2. The type 2 is the one from constant a to constat b, not the one with inifnite.

    Please tell me the steps the accomplish it. :smile:

    I know that I'm supposed to set the limits, then put it in the integral form, than FTC it. But, I'm not sure.
  2. jcsd
  3. May 5, 2005 #2
    Could you give example so I could understand question a little better.
  4. May 5, 2005 #3

    Let's say something like [int a=0 b=2] 1/(x-1)^(1/3) dx
  5. May 6, 2005 #4


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    Use the theorem of addition

    [tex] \int_{0}^{2} f(x) \ dx=\int_{0}^{1} f(x) \ dx+\int_{1}^{2} f(x) \ dx [/tex]

    You have to integrate & compute 2 limits...

  6. May 6, 2005 #5
    The limits would be 1+ and 1- right ?
  7. May 6, 2005 #6


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    It should be

    [tex] \lim_{a\nearrow 1}\int_{1}^{a} f(x) \ dx [/tex]

    [tex] \lim_{b\searrow 1}\int_{b}^{2} f(x) \ dx [/tex]

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