关于积分中值定理的证明方法

On Mean Value Theorem of Integrals

证明了积分第一中值定理中的ξ∈[a,b]可以改为ξ∈(a,b),在稍微加强部分条件的情形下,证明了积分第二中值定理中的ξ∈[a,b]也可以改为ξ∈(a,b),并简化了传统的证明方法,使得证明方法适合于非数学专业的学生。

This paper gives a new proof method for the first integral mean value theorem with ξε（a,b）. Secondly, in the case of strengthened part of the traditional conditions, it proves also the second integral mean value theorem with ξε （a, b）, the traditional proof method be changed and simplified, the new proof method is suitable for non-mathematics students