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Integral evaluated at +/- infinity

  1. Oct 29, 2009 #1
    Ok, I'm trying to solve this physics problem and I've come to the following integral ([tex]d[/tex] is taken to be some constant):

    1. [tex]\int^{+\infty}_{-\infty}{\frac{1}{(x^2 + d^2)^\frac{3}{2}}}dx[/tex]

    Now, integrating this I am supposed to get

    2. [tex]{\frac{x}{d^2\sqrt{x^2 + d^2}}}[/tex], evaluated at [tex]\pm\infty[/tex] (Sorry, don't know latex code for that).

    I don't know how to evaluate this last step. It would seem I should either get 0 or infinity, but apparently that isn't the answer. Could anyone enlighten me?
  2. jcsd
  3. Oct 29, 2009 #2


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    This is one reason why sloppiness can be bad. If you weren't thinking of it as "evaluate at infinity", you would have remembered that such improper integrals are limits... and you would have known to apply what you know about limits!
  4. Oct 29, 2009 #3


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    For large magnitude x, your expression (2.) is approx. x/[d2|x|]. You should be able to finish.
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