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Chebyshev Integral Inequality

int_a^bf_1(x)dxint_a^bf_2(x)dx...int_a^bf_n(x)dx <=(b-a)^(n-1)int_a^bf_1(x)f_2(x)...f_n(x)dx,

where f_1, f_2, ..., f_n are nonnegative integrable functions on [a,b] which are all either monotonic increasing or monotonic decreasing.

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References

Gradshteyn, I. S. and Ryzhik, I. M. Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1092, 2000.

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Chebyshev Integral Inequality

Cite this as:

Weisstein, Eric W. "Chebyshev Integral Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/ChebyshevIntegralInequality.html

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