- #1
Niles
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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?