- #1
Valour549
- 57
- 4
[tex]F(x) = \int_a^x f(t) dt[/tex]
I have found various arguments online for both.
Personally I think it's an indefinite integral because:
1) Its upper limit is a variable and not a constant, meaning the value of the integral actually varies with x. This is no different to the family of primitives represented by the indefinite integral, which also varies with x. [tex]\int f(x) dx[/tex]
2) If F is actually a definite integral then its value must be a constant, which in turn means its derivative must be zero, yet the derivative of F(x) is actually f(x) according to the Fundamental Theorem of Calculus.
Also, I found this but I think it brought more confusion than clarity.
I have found various arguments online for both.
Personally I think it's an indefinite integral because:
1) Its upper limit is a variable and not a constant, meaning the value of the integral actually varies with x. This is no different to the family of primitives represented by the indefinite integral, which also varies with x. [tex]\int f(x) dx[/tex]
2) If F is actually a definite integral then its value must be a constant, which in turn means its derivative must be zero, yet the derivative of F(x) is actually f(x) according to the Fundamental Theorem of Calculus.
Also, I found this but I think it brought more confusion than clarity.