Improper Integral Help

  • #1

Homework Statement



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.

Homework Equations



N/A.

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.
 

Answers and Replies

  • #2
34,667
6,379
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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