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Homework Help: Improper Integral Help

  1. Apr 4, 2010 #1
    1. The problem statement, all variables and given/known data

    Solve the integral [tex]\int[/tex][tex]\frac{1}{\sqrt[3]{x-1}}[/tex]. Upper limit of integration is 1 while lower limit is 0.

    2. Relevant equations


    3. The attempt at a solution

    The only thing that i'm sure about is that the antiderivative of the integral is [tex]\frac{3}{2}[/tex](x-1)^(2/3) + C. I know that i need to take the limit of the integral, but im not sure what the limit should be approaching. 1 Maybe? Since f(x) DNE there. Since i'm stuck on that, i'm kinda stuck on everything else besides the antiderivative.

    Any help would be great! Thanks.
  2. jcsd
  3. Apr 4, 2010 #2


    Staff: Mentor

    This is what you want:
    [tex]\lim_{b \to 1^-} \int_0^b \frac{dx}{\sqrt[3]{x-1}}[/tex]

    For a definite integral you don't need the constant of integration.
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