Find where an improper integral converges

  • Thread starter rocapp
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  • #1
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Homework Statement



-∞(dx/x2)

Homework Equations





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?
 

Answers and Replies

  • #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].
 
  • #3
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Thanks! I forgot that it was dependent on the function being continuous.
 

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