An extension of the Fundamental Theorem of Calculus

  • Thread starter Castilla
  • Start date
  • #1
Castilla
241
0
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.
 

Answers and Replies

  • #2
DrGreg
Science Advisor
Gold Member
2,433
1,654
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
Castilla
241
0
Oh god, it was so easy...thanks, Greg.

Castilla
 

Suggested for: An extension of the Fundamental Theorem of Calculus

Replies
14
Views
149
Replies
6
Views
1K
Replies
5
Views
115
Replies
10
Views
548
Replies
8
Views
2K
Replies
9
Views
2K
  • Last Post
Replies
12
Views
579
Replies
10
Views
1K
  • Last Post
Replies
3
Views
567
Replies
2
Views
425
Top