浅谈概率论思想在定积分中的应用

定积分是数学分析的重要内容,在各学科都有非常广泛的应用,是教学的难点与重点。求解定积分的常用方法在一些特殊情况下失效。利用概率论思想和定积分之间的内在联系,根据被积函数的特点,构造适当的随机变量,将定积分的求解问题转化为求随机变量的概率问题。利用概率论的理论体系,不仅可极大地简化运算或证明,还可解决一些用常用方法无法解决的定积分问题。

Definite integral is one of the most basic and important content in mathematical analysis,used widely in different disciplines,and is a difficult and important points of teaching.In some special case,the normal methods for solving definite integral is invalid.By using the link of probability and definite integral,and constructing proper random variables,we can transform the problem of solving definite integral into solving probability of random variables.By using the theory of probability,not only simplify greatly the solving or proof,but also solves some different integral which can not solve by normal methods.