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Ostrowski's Inequality

If $f(x)$ is a monotonically increasing integrable function on $[a,b]$ with $f(b)\leq 0$, then if $g$ is a Real function integrable on $[a,b]$,

\left\vert{\int_a^b f(x)g(x)\,dx}\right\vert\leq \vert f(a)\...
...ax_{a\leq\xi\leq b}\left\vert{\int_a^\xi g(x)\,dx}\right\vert.


Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1100, 1979.

© 1996-9 Eric W. Weisstein