定积分法求面积探究毕业论文资料.doc

定积分法求面积的探究 教 学 系： 专 业： 年 级： 姓 名： 学 号： 导师及职称： 文山学院本科毕业论文（设计） 摘 要 定积分是数学中十分重要的工具，其中求图形的面积正是它的运用之一，它的思想就是切割求和，在不同的坐标系下可采用特定的方法求解面积。本文介绍了几种运用定积分来求面积的方法，其中列举了特殊的例题以及重要的问题解决方法。如果实际问题中的所求量与某一区间有关且在该区间上具有可加性，我们就可以用函数的定积分来表示这个所求的量，因此我们就可以运用定积分来解决一些实际问题。 同时利用定积分求不规则平面图形的面积，是定积分在几何中的重要应用之一。如何灵活地运用定积分的定义及有关公式,巧妙地将求不规则图形的面积问题等价转化为求定积分的数值问题就是一大关键，本文结合实例，介绍几种常用的转化方法与求解策略。从而充分的体现数形结合的数学思想方法。 关键词：定积分；封闭图形；曲面域；对称性 Research of square in definite integral ABSTRACT A definite integral is very important mathematical tools, for which the graphics area is one of its application, its thought is to cut and, under different coordinate systems can use specific method to find the area. This paper introduces several methods of using the integral area to seek the. Which lists the specific examples and an important method to solve the problem. If practical problems for quantity with a certain interval and in the interval is additive, we can use the definite integral of a function to represent the desired amount. Therefore, we can use the definite integral to solve some practical problems. At the same time, the use of definite integrals for the irregular plane graphics area, is one of the important applications of integral in geometry. How to flexibly use definite integral is defined and the related formulae and skillfully will seek irregular graphic area equivalent transformation to calculate the numerical integral is one of key, the paper with examples, introduces several commonly used transformation method and solution strategy. In order to fully reflect the combination of the mathematical thought and method. Keywords: definite integral; closed graph; surface area; symmetry 目 录  TOC \o 1-3 \h \z \u  HYPERLINK \l _Toc419807055 一、引言  PAGEREF _Toc419807055 \h 1  HYPERLINK \l _Toc419807056 二、相关概念  PAGEREF _Toc419807056 \h 1  HYPERLINK \l _Toc419807057 1.1 定积分的定义  PAGEREF _Toc419807057 \h 1  HYPERLINK \