著者

藤田 康介 樋口 功

出版者

愛知工業大学

雑誌

愛知工業大学研究報告. A, 基礎教育センター論文集 (ISSN:03870804)

巻号頁・発行日

vol.36, pp.31-41, 2001-03-31

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Abstract. Let f(x) be continuous on the interval [a, b]. The mean value M(f) of f(x) on [a, b] is defined as follows : [numerical formula] where we denote by F(x) the primitive function of f(x). In the case when F(x) is unknown, we must calculate Ad (f) by the aid of so-called approximate formulas. In this paper, we shall obtain first an asymptotic expansion of the mean value M(f) with the terms of Riemann's quadrature by parts and next its end-points correction formula. We remark that the celebrated Euler-Maclaurin's summation formula is an immediate consequence of our asymptotic expansion just obtained. Further we shall derive some approximate formulas of mean value based on the function-values at random points.