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Chebyshev Integral Inequality

\int_a^b f_1(x)\,dx\int_a^b f_2(x)\,dx\cdots\int_a^b f_n(x)\,dx\leq (b-a)^{n-1} \int_a^b f(x_1)f(x_2) \cdots f_n(x)\,dx,

where $f_1$, $f_2$, ..., $f_n$ are Nonnegative integrable functions on $[a,b]$ which are monotonic increasing or decreasing.


Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 5th ed. San Diego, CA: Academic Press, p. 1092, 1979.

© 1996-9 Eric W. Weisstein