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Integration should blow up ?

  1. Dec 7, 2008 #1
    Using Maple 8, I integrate this:

    [tex] \int_0^1\frac{1}{\sqrt(p(1-p))} dp [/tex]

    and I get [tex] \pi [/tex]
    but, this function goes to infinity at p = 0 and 1.
    How can this be possible ?
     
  2. jcsd
  3. Dec 7, 2008 #2

    Hurkyl

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    Why wouldn't it be?
     
  4. Dec 7, 2008 #3
    The denominator has sqrt[p*(1-p)], which will give infinity on both p = 0 and 1. And so, the area under this curve is infinity too, right ?
     
  5. Dec 7, 2008 #4

    Hurkyl

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    Can you think of a reason why that should be true, though? If you're convinced the area should be infinite, then try to work out a proof of it -- such exercises are often really good at clearing up misunderstandings.

    Incidentally, it might help to play with simpler functions, e.g.

    [tex]\int_0^1 \frac{1}{\sqrt{x}} \, dx[/tex]

    or

    [tex]\int_1^\infty \frac{1}{y^2} \, dy[/tex]
     
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