计算定积分的若干方法与技巧  

Some Methods and Techniques of Calculating Definite Integral

作　　者：李东方 LI Dongfang(Department of Public Education,Xuchang Electrical Vocational College,Xuchang,He'nan Province,461000 China)

机构地区：[1]许昌电气职业学院公共教学部,河南许昌461000

出　　处：《科技创新导报》2021年第1期187-189,共3页Science and Technology Innovation Herald

基　　金：许昌电气职业学院2020年度高等职业教育教学改革研究与实践项目(项目编号:xdy20200201)资助。

摘　　要：从两个大方面阐述了计算定积分的常用方法和技巧:常规方法和特殊方法。常规方法主要包括牛顿-莱布尼茨公式、第一、二换元积分法和分部积分法,这类方法是掌握定积分计算的基础;特殊方法主要介绍了利用定积分的几何意义、被积函数的性质、构造方程组、递推关系、二重积分、级数、留数等,对其进行归纳概括,以挖掘学生的学习潜力,提高其计算定积分的核心能力。This paper expounds the common methods and techniques of calculating definite integral fromtwo aspects:conventional methods and special methods.The conventional methods mainly include NewtonLeibniz formula,the first and second variable integration method and the partial integration method,whichare the basis of mastering the calculation of definite integral;the special methods mainly introduces the use ofthe geometric meaning of definite integral,the properties of integrand function,the construction of equationsystem,recurrence relations,double integral,series,residue,etc.,and summarizes them to tap the learningpotential of students and improve their core ability of calculating definite integral.

关 键 词：定积分 被积函数 二重积分 级数 留数 

分 类 号：O172.2[理学—数学]