Cauchy-Schwarz inequality for integrals (Q117355636)

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No description defined

• Schwarz's inequality
• Buniakowsky inequality

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Language	Label	Description	Also known as
English	Cauchy-Schwarz inequality for integrals	No description defined	Schwarz's inequality Buniakowsky inequality

Statements

instance of

theorem

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subclass of

inequality

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defining formula

${\displaystyle \left(\int _{a}^{b}f(x)g(x)\,\mathrm {d} x\right)^{2}\leq \int _{a}^{b}(f(x))^{2}\,\mathrm {d} x\int _{a}^{b}(g(x))^{2}\,\mathrm {d} x}$

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in defining formula

${\displaystyle f}$

symbol represents

real-valued function

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${\displaystyle g}$

symbol represents

real-valued function

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${\displaystyle \int _{a}^{b}f(x)\,\mathrm {d} x}$

symbol represents

definite integral

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maintained by WikiProject

WikiProject Mathematics

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Identifiers

Digital Library of Mathematical Functions ID

1.7.E4

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ProofWiki ID

Cauchy-Bunyakovsky-Schwarz_Inequality/Definite_Integrals

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