浅析对称性在积分中的应用摘要 对称性的应用很广泛，其在数学，物理学，化学等方面都有体现.本文主要论述对称性在积分运算中的应用.在大学数学中积分的运算既是重点又是难点.在进行积分运算时，发现大多数题目中的积分区域是对称的或是被积函数也具有某种奇偶性.若将对称性巧妙地应用到解决这类问题中去，不仅简化了计算过程而且还节省计算时间.本文将从定积分，重积分，曲线积分以及曲面积分四各个角度入手，结合对称性在考研中的应用，深入探讨如何利用对称性解决积分问题，最后分析得出利用对称性的条件，好处，以及需要注意特别注意的一些方面.关键词 对称性 定积分 重积分 曲线积分 曲面积分Analysis on the Application of Symmetry in integralAbstract Symmetry is widely used, and it is reflected in mathematics, physics, chemistry and so on.This paper mainly discusses the application of symmetry in integral operation.In college mathematics, the operation of integral is both the key point and the difficulty.In the integral operation, it is found that the integral region of most problems is symmetrical or the integrand function also has some kind of parity.If the symmetry is cleverly applied to solve such problems, it not only simplifies the calculation process but also saves the calculation time.This paper will start from four angles of definite integral, heavy integral, curve integral and curvature area, combined with the application of symmetry in the examination and study, how to solve the integral problem by using symmetry, and finally analyze the conditions, benefits and some aspects that need to be paid attention to in particular attention.Key words symmetry definite integral double integral Curve integral Surface integral目1录引言.......................................................................................................................11 对称性在定积分计算中的应用......................................................................
