An extension of the Fundamental Theorem of Calculus

[Castilla]

In a book of Introduction to Probability I found this statement:

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

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

Thanks.

 

[DrGreg]

In a book of Introduction to Probability I found this statement:

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

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

Thanks.

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

for any constant a < x. So the answer is yes.

 

[Castilla]

Oh god, it was so easy...thanks, Greg.

Castilla