对称性在积分计算中的应用

Application of Symmetry in Integrals

积分计算是高等数学的重要内容之一。在计算积分的过程中,若不能掌握正确的方法和技巧,往往会把简单的问题复杂化。通过分析积分区域的对称性、被积函数的对称性及积分变量的轮换对称性,给出一些重要的结论,并将其应用到积分计算中。

Integral is one of the important contents of advanced mathematics. In the process of calculating in-tegrals, simple problems are often complicated if the correct methods and techniques are not mas-tered. By analyzing the symmetry of the integration region, the symmetry of the product function and the rotation symmetry of the integral variable, some important conclusions are given and ap-plied to the integral calculation.