关于定积分定义及可积条件的讨论  

The Definition of Definite Integral and Discussion of the Condition of an Integrable Function

作　　者：柳洁冰[1] 张宏亮[2] 

机构地区：[1]张家口教育学院数学系,河北张家口075000 [2]河北建筑工程学院,河北张家口075000

出　　处：《科教文汇》2011年第7期69-70,共2页Journal of Science and Education

摘　　要：教材在定积分的定义中,通常特别强调分法和选取的两个任意性。利用此定义讨论问题比较繁琐,因此在此定义基础上做出进一步讨论,即将定义中分法的任意性用特殊分割来代替,这样不仅给解决问题带来了方便,而且可以帮助大家更深刻地理解和掌握定积分定义的实质。同时还给出了一个可积的充分必要条件,即关于函数收敛的Cauchy收敛准则,但应用此定理证明关于函数的可积性问题相当麻烦,由此我们对该定理做出改进,得出一个简单易行的判定定理。The textbooks stress the arbitrary choice between the partition T and in the definition of definite integral,but it seems cumbersome to discuss issues with this definition .Therefore, this paper replace the partition T with a special partition in the definition on the base of further discussions.This method is not only convinent to settle issues in practice,but also helpful for the reader to gain a deep understanding and master the essence of the definite integral.Meanwhile,this paper gives an integrable necessary conditions--the Cauchy criterion for convergence.At last,this paper makes a simple theorem with improvements because the fact that the application of the definition to prove the integrable issues of a function appears cumbersome.

关 键 词：定积分 分割 CAUCHY 收敛准则 

分 类 号：O172.2[理学—数学]