留数在实积分中的应用摘要 本文主要利用留数方法研究实积分的计算问题。虽然解决积分的计算问题有许多方法，但在积分的计算过程中，有些积分在实数范围内并不能被计算出来，需要一种新颖、独特的计算方法，即留数方法。在复分析中，留数定理是用来计算积分的一个有力的工具，有些用解析方法难以求得的实积分，相较而言用留数方法计算的效果更好，尤其是对原函数不易直接求得的定积分与反常积分，是一个非常有效的方法，主要是将原积分转化为沿闭曲线的路径积分，之后计算出各个孤立奇点处的留数，将积分的计算转化为留数的计算，得到积分的解，以达到简化积分计算的目的，这一过程体现了留数方法在实积分计算中的重要地位，为积分理论的发展奠定了一定的基础。关键词 留数；实积分；留数定理；解析函数The application of residues in real integralsAbstract This paper mainly studies the calculation of real integrals by using the residue method. Although there are many methods to solve the problem of integral calculation, in the process of integral calculation, some integrals cannot be calculated in the real number range, which requires a new and unique calculation method, that is, residue method. In complex analysis, the residue theorem is used to calculate the integral of a powerful tool, some with analytical methods are difficult to obtain real points, compared with residue method to calculate the effect is better, especially for the function is not easy to directly obtain the definite integral and improper integral, is a very effective method, mainly to the original integral into path integral along a closed curve, then calculate the residue, each isolated singularity integral calculation can be converted to the calculation of residue, obtain the integral solution, to achieve the purpose of simplified integral calculation, the process reflects the residue method in the important position of real integral calculation, It has laid a certain found...
