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Improper Integrals

  1. Mar 31, 2004 #1
    Why are these two integrals undefined?
    1) [tex] \int_{-1}^{1} \frac{\,dx}{x^{\frac{4}{3}}} [/tex]

    2) [tex] \int_{3}^{6} \frac{\,dx}{5-x} [/tex]

    I got real answers for both, the first one 0, and the second one ln(2), but I think I'm in serious violation of the Fundamental Theorem of Calculus.
  2. jcsd
  3. Mar 31, 2004 #2
    division by zero - notice that x = 0 blows up the first integrand and x = 5 the second one likewise. Even with these points excluded, you get pretty big answers (not the answers that you got). Infinity in fact.
  4. Mar 31, 2004 #3


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    texing these is tricky, have a look at the source for these!

    [tex] \int_{-1}^{1} \frac{\,dx}{x^{\frac{4}{3}}} = \frac{x^{\frac{-1}{3}}}{\frac{-1}{3}}|^1_{-1}[/tex]


    The problem is that the function crosses over an asymtote. What happens when x is 0? Is the function infinity? How do you add infinity?

    [tex] \int_{3}^{6} \frac{\,dx}{5-x} = -\ln|5 - x| |^6_5[/tex]

    That log function there, what happens when x = 5? What exponent on e will give you a value of 0?
    Last edited: Mar 31, 2004
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