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Comparison Test: Am I using a good comparison function?

  1. Nov 9, 2011 #1
    1. The problem statement, all variables and given/known data
    Does the following interval diverge?
    [itex]\int^9_1 \frac{-4}{\sqrt[3]{x-9}}[/itex]

    2. Relevant equations

    3. The attempt at a solution
    Well.. I've used the following function that I think is always less than the above function to prove that the function above DOES NOT diverge (by showing that the function below converges). I'm just wondering if this is an appropriate way of telling that the function above does not diverge...

    [itex]\int^9_1 \frac{-4}{x-9}[/itex]
  2. jcsd
  3. Nov 9, 2011 #2


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    Science Advisor
    Homework Helper

    You don't need a comparison test. You can integrate that function. Just treat it as an improper integral. Integrate from 1 to M and let M approach 9.
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