二重积分的“变量替换”问题

The Study on Variable Substitution of Double Integral

二重积分的概念和计算是多元函数微积分学的一个重点,变量替换法是计算二重积分的重要方法.新变量的选取是否恰当是简化积分运算的关键.结合例题,从简化被积函数及积分区域方面较详细地介绍了新积分变量的选取方法.

The concept and calculation of the double integral is one of the focuses of the multivariate function calculus,and the variable substitution method is an important method to calculate the double integral.Selecting appropriate new variable is the key to simplify integral computation.In this paper,method for selecting new integral variable is illustrated by examples through simplifying of the integrand and the integral area.