# Thread: Proving function is not integrable

1. ## Proving function is not integrable

S(x) = x - n where n<= x <= n+1

How do I show that there is no function F such that F'=S?

2. ## Re: Proving function is not integrable

Originally Posted by BrownianMan
S(x) = x - n where n<= x <= n+1

How do I show that there is no function F such that F'=S?
S(x) is known as 'fractional part of x'...

Fractional Part -- from Wolfram MathWorld

... and it seems not to exist a valid reason for which it is not integrable...

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$

3. ## Re: Proving function is not integrable

Originally Posted by BrownianMan
S(x) = x - n where n<= x <= n+1

How do I show that there is no function F such that F'=S?
$\displaystyle S$ can't be a derivative because it has jump discontinuities at $\displaystyle \mathbb{Z}$, and derivatives satisfy the mean value property. On the other hand it's integrable over any bounded interval. I suggest youu review what the fundamental theorem of calculus actually says.