积分第一中值定理

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。

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 .

微分中值定理与积分第一中值定理的关系

The Relationship Between Differential Mid-value Theorem and the Frist Intergration Mid-value Theorem

关于积分第一中值定理的一些探讨

Some Probing of Intermediate Value Theorem in Integral

本文就积分第一中值定理给出了一个简单的证明。

This paper gives a simple proof of the first mid - value theorem of Integral .

对微分中值定理和积分第一中值定理的关系进行了探讨。

This paper has studied the relationship between the differential mid-value theorem and the first intergration mid-value theorem .

证明关于积分第一中值定理的中间点ξ的渐近性质的一般结果。

The general result of the asymptotic property of the intermediate value of the mean value theorem for the integrals is proved .

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。

Study about the first mean value theorem for integrals , which obtain a new results on the mean value asymptotic behavior .

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。

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。

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 .

二重积分的第一中值定理

He first mean value theorem of the double integrals

通过构造积分上限函数，给出积分第一中值定理的另一证法，并结合微积分中值定理证明积分等式、积分不等式与定积分的中值命题。

The essay builds the integral upper limit function to obtaining other proof about theorem of integral first median value , and combine with theorem of calculus median value to proving Integral equality , inequality and median proposition .

对积分中值定理中间点的渐近性进行研究，给出了推广的积分第一中值定理的中间点的渐近性的一个公式。

This paper presents a generalization of mean value theorem for integrals and discusses the asymptotic properties of mean value of mean value theorem for integral .