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Integral Question

  1. Sep 17, 2004 #1
    Hello everyone! Can anyone tell me a formula (or a way to derive) this integral?
    [tex]\int|f(x)|dx[/tex]
    where [tex] f(x) [/tex] is a real, continuous function of x in the vector space [tex]C^\infty[/tex]. So far, all I've figured out is that odd-order integrations are related to the signum function.
    Thanks!
     
  2. jcsd
  3. Sep 17, 2004 #2
    Derive or find the area under |f(x)|?

    |f(x)| = f(x), if x >=0; -f(x), if x<0

    so &Int; |f(x)| dx has 2 solutions: F(x), and -F(X), where F(X) is the antiderivative of f(x).
     
  4. Sep 17, 2004 #3

    Tide

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    No, |f(x)| = f(x) if f(x) >= 0 and -f(x) if f(x) < 0.

    I recommend breaking up the integral into separate domains as I've indicated and integrating piecewise.
     
  5. Sep 18, 2004 #4
    Stop repeating my answers :p
     
  6. Sep 18, 2004 #5

    Tide

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    LoL! Man, I've just GOTTA get some reading glasses! :bugeye:
     
  7. Sep 18, 2004 #6
    He wasn't repeating your answers. Prudens used x, while Tide correctly used f(x).
     
  8. Sep 18, 2004 #7
    what i really meant was f(x)... but i was thinking about beer.
     
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