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An extension of the Fundamental Theorem of Calculus

  1. Sep 23, 2005 #1
    In a book of Introduction to Probability I found this statement:

    " Let be [tex]F(x) = \int_{-\infty}^{x} f(t)dt.[/tex] Then, by the Fundamental Theorem of Calculus, [tex]F'(x) = f(x).[/tex]"

    With the minus infinity on the lower limit, it is this a valid aplication of the FTC???

    Thanks.
     
  2. jcsd
  3. Sep 23, 2005 #2

    DrGreg

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    [tex]F(x) = \int_{-\infty}^{a} f(t)dt + \int_{a}^{x} f(t)dt[/tex]

    for any constant a < x. So the answer is yes.
     
  4. Sep 23, 2005 #3
    Oh god, it was so easy...thanks, Greg.

    Castilla
     
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