一道含参变量积分考研真题的推广及应用

Popularizing and Application of a Question About Parametric Integration from the Postgraduate Entrance Examination

含参积分是数学分析课程的难点,在历年考研真题中层出不穷.通过把一道考研真题进行推广,讨论与其相关的题型的证明方法,及运用此方法解决其它学校相关的考研真题,以给广大数学爱好者一些启发.

Parametric integration is indeed a difficult point in the course of mathematical analysis,which has appeared many times in the postgraduate entrance examination over the years.The paper takes a question from the postgraduate entrance examination as the background,explores its source,discusses the types of questions and methods of the proof related to them and uses the method to solve some questions from other universities,so as to offer some inspiration to Mathematics majors.