定积分微元法的应用探讨

Exploration of the Application of Differential Element Method of Definite Integral

摘要: 微积分能够广泛应用于各个领域来改变我们这个世界，得益于应用它解决问题的思想方法——微元法。本文分析了定积分微元法的主要思想，总结了定积分微元法的使用条件及方法，并通过三种分割方法求面积，分析总结微元法的难点和使用原则，并解决了旋转体的体积和抽取液体做功两个问题。该方法类似可推广到其他几何、物理及经济问题。

Abstract: Calculus can be used in a wide range of fields to change our world, thanks to its application to solve problems of thought—the element method. In this paper, the main idea of the definite integral element method is analyzed, the conditions and methods of using the definite integral element method are summarized, and the area is obtained by three segmentation methods, the difficulties and principles of the method are analyzed and summarized, and the two problems of the volume of the rotating body and the extraction of liquid to do work are solved. The method can also be extended to other geometric, physical and economic problems.