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Find where an improper integral converges

  1. Oct 19, 2012 #1
    1. The problem statement, all variables and given/known data

    -∞(dx/x2)

    2. Relevant equations



    3. The attempt at a solution

    ∫(dx/x2) = -1/x

    (-1/∞) - (-1/-∞) = 0

    However, the answer is that the integral diverges. Why is this the case?
     
  2. jcsd
  3. Oct 19, 2012 #2

    jbunniii

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    The function [itex]1/x^2[/itex] grows infinitely large as [itex]x \rightarrow 0[/itex], so you have to break this into two improper integrals:
    [tex]\int_{-\infty}^{0} dx/x^2 + \int_{0}^{\infty} dx/x^2[/tex]
    You can easily check that both of these integrals diverge to [itex]\infty[/itex].
     
  4. Oct 21, 2012 #3
    Thanks! I forgot that it was dependent on the function being continuous.
     
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