- #1

Niles

- 1,866

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## Homework Statement

Hi guys

From the Fundemental Theorem of Calculus we know that if we have a continuous function f : [a,b] ->

**R**and

*F*is the function on (a,b) defined by

[tex]

F(x)=\int_a^xf(t)dt,

[/tex]

then

*F*is differentiable on (a,b) with F'(x)=f(x) for all x in (a,b), i.e.

[tex]

\frac{d}{dx}\int_a^x f(t)dt=f(x).

[/tex]

**Question**: Is it correct also to write

[tex]

\frac{d}{dx}\int f(t)dt=f(x)?

[/tex]

If not, then is there a way of expressing [itex]\frac{d}{dx}\int_a^x f(t)dt=f(x)[/itex] without limits on the integral?