摘要:本文对定积分的微元法进行了系统地阐述,主要研究内容是通过运用定积分的微元法解决一些几何上求平面图形面积、求旋转体体积、求曲线弧长；物理上做功、液体对平面薄板压力、转动惯量；存储论; 医药卫生工作中的几个数学建模应用等问题，来体现数学分析的一些思想观点和方法.从而能够用积分学的观点处理几何、物理、医学等问题,使解题更简洁，拓宽解题思路 ,提高解题能力.

关键词：定积分；微元法；应用

Abstract:This article on differential element method of integral systems formulated main research content is through the use of definite integrals on differential element method of solving some of the geometric plane graphic area, seeking rotating object volume, arc length of the curve; Physical stress, moment of inertia, liquids on planes doing work on thin plate; Storage first; Medical and health work of several issues such as application of mathematical modeling, to reflect some of the ideas and methods of mathematical analysis. So as to be able to view geometry of integral calculus, physics, medicine, and other issues, solve problems more concise, broaden the way of solving problems, improving the ability of solving problems.

Key words:  Definite integral;  Differential element method;  Application

　　在科学技术领域中，有大量的问题，定量求解它们的途径都可以归结为一种和的极限的运算，这种运算，经过数学抽象，就成为定积分概念。这类问题，在几何、物理、存储论、医药卫生中比比皆是，也就是说，在几何、物理、存储论、医药卫生中，有不少量，可以借助于微元法来计算其满足某种条件的数值大小或分析其作为变量的变化区间和变化规律。换句话说微元法思想在定积分的应用中占有很重要的地位。