摘 要多重积分的形式是各种各样的，掌握其计算方法及技巧是解答问题的关键。本文主要从直角坐标、坐标变换、对称性、分部积分法、转化成曲线积分或曲面积分等方面讨论了二重积分及三重积分的几种计算方法和技巧，并分别举例说明。此篇论文较为全面地总结了多重积分的计算方法，而且剖析了各种方法在运用中的常见错误，希望能够给初学者提供一定的借鉴作用。关键词：二重积分；三重积分；计算方法I AbstractThe form of multiple integral is various. Mastering calculation methods is the key to solve problems. This paper mainly discusses several calculation methods of double integral and triple integral, from every aspects such as rectangular coordinates, coordinate transformation, symmetry, integration by parts, converting curvilinear integral or surface integral and so on, meanwhile giving some examples respectively. This paper more comprehensively summarizes the calculation methods of multiple integral, and analyzes the common errors in the use of various methods, hoping to provide certain reference for beginners.Keywords: double integral; triple integral; calculation methodsII 目 录摘 要.......................................................IABSTRACT.....................................................II1. 引言.......................................................12. 二重积分的计算方法........................................12.1 直角坐标系下二重积分的计算...............................12.2 用变量变换法计算二重积分.................................62.3 用极坐标计算二重积分.....................................82.4 对称性在二重积分计算中的应用............................132.5 用分部积分法计算二重积分................................152.6 曲线积分在二重积分计算中的应用..........................163. 三重积分的计算方法.......................................173.1 直角坐标系下三重积分的计算..............................173.2 用变量变换法计算三重积分................................223.3 用柱面坐标计...
