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Ostrowski's Inequality


If f(x) is a monotonically increasing integrable function on [a,b] with f(b)<=0, then if g is a real function integrable on [a,b],

 |int_a^bf(x)g(x)dx|<=|f(a)|max_(a<=xi<=b)|int_a^xig(x)dx|.

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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. 1100, 2000.

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Ostrowski's Inequality

Cite this as:

Weisstein, Eric W. "Ostrowski's Inequality." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/OstrowskisInequality.html

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