Probabilistic Computation Method for Some Types of Integral

doi:10.3696/j.issn.1672-6952.2012.04.025

Journal of Liaoning Petrochemical University ›› 2012, Vol. 32 ›› Issue (4): 95-98.DOI: 10.3696/j.issn.1672-6952.2012.04.025

Probabilistic Computation Method for Some Types of Integral

YU Jing-xian, LI Jin-qiu, MIAO Chen

School of Sciences, Liaoning Shihua University, Fushun Liaoning 113001, P.R.China

Received:2011-12-30 Published:2012-12-20 Online:2017-07-06

几种特殊类型积分的概率计算方法

于晶贤，李金秋，苗　晨v

辽宁石油化工大学理学院，辽宁抚顺１１３００１

作者简介:于晶贤（１９８２－），男，辽宁丹东市，讲师，硕士。

Abstract

Abstract:

Considering the complexity and infeasibility of Newton-Leibniz formula in computing some types of integral, it was used the density functions and numerical characteristics of exponential distribution, normal distribution and chi-square distribution to compute three types of integral in calculus. Three computational formulas were got. Through the process of proof, it was found that the convenience of probabilistic method and close relationship between probability theory and calculus.

Key words: Normal distribution , Exponential distribution , , Chi-square distribution , Numerical characteristics , Probabilistic method

摘要： 　考虑到利用牛顿－莱布尼茨公式求解某些类型积分的复杂性和不可行性，利用概率论中指数分布、正态分布和卡方分布的概率密度函数与数字特征，对微积分中三种特殊类型的积分进行了计算，得到了这３种特殊类型积分的计算公式，体现了概率方法在计算某些类型积分时的简便性，进而也从一个侧面体现了概率论与微积分之间的紧密联系。

关键词: 　正态分布, 　指数分布, 　卡方分布, 　数字特征, 　概率方法

YU Jing-xian, LI Jin-qiu, MIAO Chen.

Probabilistic Computation Method for Some Types of Integral

[J]. Journal of Liaoning Petrochemical University, 2012, 32(4): 95-98.

于晶贤，李金秋，苗　晨. 几种特殊类型积分的概率计算方法[J]. 辽宁石油化工大学学报, 2012, 32(4): 95-98.

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Probabilistic Computation Method for Some Types of Integral

几种特殊类型积分的概率计算方法

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