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2008•Journal of South China Normal UniversityRequires access

ON THE FIRST MEAN VALUE THEOREM OF INTEGRAL

Yijun Chen

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Abstract

With the fundamental theorem of calculus as a bridge,by using some important results from the function theory of real variables and Weierstrass's first theorem with Bernstein's proof in the approximation theory,some stronger results than the classical first mean value theorem of integral are obtained,which reveal the deep relation between the first mean value theorem of integral and the mean value theorems of differential.

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What this paper is about

With the fundamental theorem of calculus as a bridge,by using some important results from the function theory of real variables and Weierstrass's first theorem with Bernstein's proof in the approximation theory,some stronger results than the classical first mean value theorem of integral are obtained,which reveal the deep relation between the first mean value theorem of integral and the mean value theorems of differential.

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Available abstract

With the fundamental theorem of calculus as a bridge,by using some important results from the function theory of real variables and Weierstrass's first theorem with Bernstein's proof in the approximation theory,some stronger results than the classical first mean value theorem of integral are obtained,which reveal the deep relation between the first mean value theorem of integral and the mean value theorems of differential.

Key concepts: Mean value theorem (divided differences), Fundamental theorem of calculus, Mathematics, Fundamental theorem, Kelvin–Stokes theorem, Green's theorem, Picard–Lindelöf theorem, Mean value

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