Category:Darboux's Theorem

This category contains pages concerning Darboux's Theorem:

Let $f$ be a real function which is continuous on the closed interval $\closedint a b$.

Let $\ds \int_a^b \map f x \rd x$ be the definite integral of $\map f x$ over $\closedint a b$.

Then:

$\ds m \paren {b - a} \le \int_a^b \map f x \rd x \le M \paren {b - a}$

where:

$M$ is the maximum of $f$

$m$ is the minimum of $f$

on $\closedint a b$.

Source of Name

This entry was named for Jean-Gaston Darboux.