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Homework Help: Comparison test on second species integrals

  1. Dec 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Determine if the following integrals are convergent or divergent. Explain why.

    [itex]\int^{1}_{0} \frac{1}{1-x^{4}} dx[/itex]

    3. The attempt at a solution
    I've tried using Comparison Test, using [itex]f(x) = \frac{1}{1-x^{4}} and\; g(x) = \frac{1}{1-x}[/itex], [itex]0 \leq f(x)\leq g(x)[/itex] [itex]in ] 0,1 [ [/itex] and I know [itex]g(x)[/itex] is divergent. My question is if its plausible that, by using Comparison Test, if [itex]g(x)[/itex] is divergent, will [itex]f(x)[/itex] be divergent too?
  2. jcsd
  3. Dec 23, 2012 #2


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    No. Not plausible. You want a divergent integral that's less than f(x), not greater. Hint: factor 1-x out of (1-x^4).
  4. Dec 23, 2012 #3
    It was my first thought, but I considered it too simple to be true, thanks!
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