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Homework Help: Simple Improper Integral Question (just a question of concept understanding)

  1. Mar 1, 2010 #1
    1. The problem statement, all variables and given/known data

    I am to determine whether the following integral is convergent or divergent

    [tex]
    \int_0^1 \frac{sin(x)}{x}
    [/tex]

    From what I hear since, lower limit is zero there is a removable discontinuity.
    Thus just because of this, it is convergent? Can someone let me know if this
    is correct.
     
    Last edited: Mar 1, 2010
  2. jcsd
  3. Mar 1, 2010 #2
    Do you know that:

    [tex]lim(x->0) \frac{sin(x)}{x}=1[/tex]

    ?

    If yes, then you can see that the function is bounded on the interval and therefore integrable.
     
  4. Mar 1, 2010 #3
    Oh thanks!
     
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