積分の平均値の定理の拡張

Abstract

Let f(x) be continuous on the closed interval [a, b]. By the mean value theorem of integral, there exists a point ξ on [a, b] satisfying [numerical formula] In other word, we can find a point ξ∈[a, b] such that the straight line l defined by y=f^^～(x)=f(ξ) passing the point (ξ, f(ξ) and Parallel to the x-axis satisfies y = f^^～(x) [numerical formula] The aim of the present paper is to generalize the above mean value theorem of integration. First, we shall prove the following