积分中值定理

文章在第一积分中值定理的条件下，证明了介值点ξ必可在开区间（a，b）内取得，并且给出以上结果的一些应用。

This paper proves that the point ζ must be in the open interval ( a , b ) under the conditions same as in the first mean value theorem of integrals , and gives some applications of the above results .

文章从积分中值定理的几何特征出发，对该定理作了一点补充说明，并通过实例进一步验证了这种改进的优点。

A complement to the mean value theorem of integrals is gained by analyzing the geometric characteristic of the mean value theorem of integrals .

本文不仅证明了下面的第一积分中值定理：定理设1）函数f（x）在[a，b]上连续；

In this paper the following result is proved : Theorem Let 1 ) f ( x ) be Continuous over Closed interal [ a , b ] ;

本文讨论了积分中值定理的中间点ξ的渐近性质，从而得出对于不同积分中值定理，当b→a时，ζ势向不同位置。

In this paper , the asymptotic property of the " inter-point ξ" in mean value theorems of integrals is discussed . We get the conclusion that for different mean value theorems of integrals , ξ approaches different positions as b → a.

将Rn中积分中值定理的中值点取值范围，由积分区域D上缩小到D的内部D/D上取到。

This paper makes the range of integral mid-value point in Rn narrowed from integral region D to the inside of D / D .

积分中值定理在广义Riemann积分中的推广广义留数定理在计算某类广义积分中的应用

An Extension of the First Mean Value Theorems for Generalized Riemann Integration ; The Application of Generalized Residue Theorm in Calculating a Certain Kind of Generalized Integral

由一个定理的结论，给出Lagrange中值定理，Cauchy中值定理，积分中值定理和Taylor中值定理的统一证明及一个计算待定型极限的方法。

In this article , from one conclusion of one theorem , uniform proof for theorem of mean of Lagrange , Cauchy , integral and Taylor is given . Meanwhile one method of calculation for undefined limit is given too .

对积分中值定理的中值极限估计式的研究

On the Limit Estimation Formula of Midvalue in the Integral Mean Value Theorem

积分中值定理的逆问题及渐近性

On inverse problem of the Mean Value Theorem for integral and its approachability

关于积分中值定理的中间值的渐进性质

The asymptote behavior of intermediate point in the Mean Value Theorem for integrals

推广的积分中值定理中的中值ξ的渐近性

A Discussion of Asymptotic Property of Median in the Popularized Integral Median Theorem

关于积分中值定理的证明

On The Proofs of the Mean-Value Theorem of Integrals

关于积分中值定理中中间点的进一步估计

The approaching state of mean points for the first integral mean value theorem

关于积分中值定理中间值的探讨

On the Middle Value of Integration Middle Value Theory

简化形式的积分中值定理另一种表述

Another Indication of the Simplified Form of Mean Value Theorem for the Integrals

关于二重积分中值定理的一个推广

An Extension of Double Integral Mean Value Theorem

其一，积分中值定理，它可以将定积分转化为函数值；

Firstly , mid-value theorem of integration can transform definite integration to functional value ;

积分中值定理的推广

The extension of intermediate value theorem of integral

关于推广的积分中值定理中间点渐近性

On the general mean value theorem for Integrals

积分中值定理的两个结果

Two Results of Twofold Integral Median Theorem

积分中值定理的中值渐近性的又一定理

A Theorem of the Mean Value Asymptotic Behavior of the Mean Value Theorem for Integrals Again

关于积分中值定理中值点位置的估计

The Estimation of the Location on the Mean Points of the Theorems of Mean Integral Calculus

本文主要讨论了第二积分中值定理中值点的渐近速度。

This paper discusses the asymptotic rate of mean value point in second mean vaule theorem for integrals .

关于第一类不连续点函数的介值定理和积分中值定理

The Intermediate Value and Mean Value Theorem for Integral for Functions with Discontinuity Points of the First Kind

关于曲线积分中值定理中间点的一个一般性结果

A More Universal Result on the Intermediate Point in the Mean Value Theorem for First Form Curve Integrals

广义积分中值定理与积分中值定理中间点渐近性基本定理

Asymptotic Characteristic Basic Theorems of the Intermediate Point between the Generalized Integral Mean-value Theorems and the Integral Mean-value Theorems

以积分中值定理与水平力平衡条件确定了辊模压力。

The roller die pressure is set up with the integral mid-value law and the horizontal force balancing condition .

得到了第二积分中值定理的中间点渐近性质的重要结果是

He authors obtained important results of the asymptotic property of the mediant for the second integral mean-value theorem as follows

最后同样给出了积分中值定理的一个相关问题，然后给出了较为复杂的证明过程。

In the end , the author also gives the opposite question of the calculus mean value theorem and the complicated proofs .

利用本文证明的结论，对积分中值定理的中值ξ的渐近性也得出了类似的结论。

With the conclusion , a similar conclusion is reached by analyzing the asymptotic property of median in the integral median theorem .