积分变换在广义积分中的应用

The application of integral transformation in generalized integrals

在高等数学学习中,有些广义积分的计算过程是比较繁琐的,有些可能因为其原函数不是初等函数而无法计算.利用Fourier变换和Laplace变换的定义、性质及相关结论,研究了∫+∞0sinx/xdx,∫+∞0e-x2dx等广义积分值的计算,简化了此类广义积分的计算.

In the study of advanced mathematics,it is onerous for some processes of improper integral,and some of which may lead to incalculable due to its non-elementary function of original form.By using of the definition,property and related conclusionabout the Fourier transform and Laplace transform,researches on the calculation of improper integral such as[0,+∞]∫sinxdx/X,[0,+∞]∫[e^(-x)2]dx,it makes improper integral much easier.