重积分的变量变换及其在积分计算中的应用

Transformation of Multiple Integral and Its Application in Integral Calculation

摘要: 重积分在高等数学中占有重要的地位，在工程技术中有着重要的应用。本文在二重积分和三重积分变量变换方法的基础之上，讨论了区域由两族曲线围成时二重积分的变换方法及区域由三族曲面围成时三重积分的变换方法等，并将此类方法应用于解决考研中复杂的重积分计算问题。

Abstract: Multiple integral plays an important role in Higher Mathematics and has an important application in engineering technology. On the basis of the transformation methods of double integral and triple integral variable, this paper discusses the transformation methods of double integral when the region is surrounded by two families of curves and triple integral when the region is surrounded by three families of surfaces, etc., and all kinds of variable transformation method is applied to solve Postgraduate entrance examination questions.