An extension of the Fundamental Theorem of Calculus

  • Thread starter Castilla
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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.
 

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  • #2
DrGreg
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Castilla said:
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.

[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.
 
  • #3
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Oh god, it was so easy...thanks, Greg.

Castilla
 

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