In this paper,we prove the first mean value theorem for definite integrals newly,introduce some betterment with its applications of the first mean value theorem for definite integrals.
本文重新表述了定积分第一中值定理的证明,并改进了该定理,对于改进了的定积分第一中值定理还给出了证明及一些应用实例。
Using variable upper limit integration and Lagrange mean value theorem,this article proves the first mean value theorem under the same condition and give several spread of the first integral mean value theorem.
在条件完全相同的情况下改进积分第一中值定理,并利用变上限积分函数和拉格郎日中值定理证明该定理,并给出积分第一中值定理的几个推广。
In this paper, the first integral mean value theorem is im proved under the same conditions.
对积分第一中值定理在完全相同的条件下进行了改进和加强 ,并给出了应用举例 。
Two kinds of generalizations of the first mean value theorem of integral for integrable functions with different properties are established in the paper,the results extend the previous conclusions.
本文建立了两类可积函数的积分第一中值定理的推广形式,推广了已有结论。
The continuity condition is weakened to the condition with intermediate value property in the first mean value theorem of integral,the generalized versions of the first mean value theorem of integral for functions with intermediate value properties are established.
将积分第一中值定理中的连续性条件减弱为有介值性,建立了具有介值性质的可积函数的积分第一中值定理的推广形式。
The author discussed analyzing property on the "middle point" of the first mean value theorem for integrals and the promoted first mean value theorem for integrals by adding conditions,and proved the "middle point" is continuous and differential.
研究了第一积分中值定理"中值点"ξ和推广的第一积分中值定理"中值点"ξ的分析性质,证明了ξ具有连续性和可导性。
In this paper, we discuss the inverse problem of the first mean value theorem for integrals and (approachability) in the inverse problem.
讨论第一积分中值定理的逆问题及其渐近性。
In this paper,the first integral mean value theorem and the generalized first integral mean value theorem are improved in traditional teaching materials.
文章针对传统教材中的“第一积分中值定理”和“广义第一积分中值定理”进行了改进,通过列举若干典型题目,应用改进后的定理简明扼要的处理了这些问题。
The Proof about the First Integral Mean Value Theorem;
关于积分第一中值定理的证明和推广
On Extension of the First Mean Value Theorems for Generalized Riemann Integration;
积分第一中值定理在广义Riemann积分中的推广
Study about the first mean value theorem for integrals, which obtain a new results on the mean value asymptotic behavior.
研究积分第一中值定理，获得了其中值渐近性的一个新结果。
Analyzing Property on the "Middle Point" of the First Mean Value Theorem for Integrals;
第一积分中值定理“中值点”ξ的分析性质
A Further Research on Intermediate Point in the Second Mean Value Theorem for Integrals
积分第二中值定理的中值点ζ的进一步研究
On Asymptotic Property of the Mid-Point of Mean Value Theorem for First Form Curvilinear Integral;
第一型曲线积分中值定理“中间点”的渐近性
On the Asymptotic Properties of the Intermediate Point in the Mean Value Theorem for First Form Curve Integral;
关于第一类曲线积分中值定理“中间点”的渐近性
On Asymptotic Approximation of the Second Mean Value Theorem of Integrals;
再论积分第二中值定理中值的渐近性
Asymptotic Properties for the "Middle Point" of the Second Mean Value Theorems of Integral
积分第二中值定理“中间值”的渐近性
The Theorem of "Middle Point"in the Second Integral Mean Value;
积分第二中值定理“中间点”的渐近性
A Use of Lagrange Middle-Value Theorem;
Lagrange中值定理的一个应用
Another Proof of Lagrange Mean Value Theorem;
Lagrange中值定理的一个证明
General Form of Lagrange Mean Value Theorem
Lagrange中值定理的一般形式
STRONG LAW OF THE MEAN FOR MEASURE-UNITYOF THE LAWS OF THE MEAN FOR CALCULUS;
测度强中值定理──微积分中值定理的统一
Rolle's theorem is a special case of the mean value theorem.
罗尔定理是中值定理的一种特殊形式。
Asymptoticy and Error Estimation for “the Middle Point”of the Second Integral Mean Value;
第二积分中值定理“中间点”的渐进性及误差估计
The Research for Asymptotic Property of Intermediate Value in the Second Mean Value Theorem for the Integrals
积分第二中值定理“中间点”的渐进性研究
This paper is devoted to studying the asymptotic behavior of the intermediate point in the mean value theorem for first form curve integrals. A general result is obtained.
讨论了第一类曲线积分中值定理“中间点”的渐近性质，得到了更具一般性的新结果。