一类三重积分的新算法

主要讨论有关某一类的三重积分的计算问题。积分是微积分学与数学分析里的一个非常重要的核心概念,积分的运算方法也因此一直被不断的总结与研究。随着积分变量的增加,重积分就变的更加难以计算。三重积分的计算问题更一直被很多人所关注,一般情况下是把三重积分化为三次定积分来计算。近年来,出现了一些新的方法和手段去解决三重积分的计算问题,这里提出一种结合《概率论与数理统计》的相关内容,根据服从0-1]区间上均匀分布的顺序统计量的有关知识,利用顺序统计量的数学期望以及条件数学期望,直接把三重积分的计算变为一重积分的计算方法,进而达到简化计算三重积分的目的。

New method for a kind of triple integrals

This paper considers one kind of triple integral calculation problem.Integral calculus is a very important core concept in mathematical analysis,the arithmetic method of integral also has been constantly summarized and studied.With the increase of integral variable,multiple integral becomes even more difficult to calculate.Triple integral calculation has always been concerned by many people,in general people turn triple integral into cubic definite integral.In recent years,there have been some new methods and means to solve the calculation problem of triple integral.So the author combined with knowledge about the probability and mathematical statistics,and according to order statistics from a uniform distribution on 0,1],turns directly the triple integral calculation into a definite integral calculation by taking advantage of the mathematical expectation and conditional expectation,then achieves the goal of simplified triple integral calculation.