论文定积分元素法.doc

2012 届学士学位论文 定积分的元素法及其应用 系 别: 数学系 专 业: 数学与应用数学 学 号: 姓 名: _ 指 导 教 师: 指导教师职称: 定积分的元素法及其应用 摘要 合理选取积分元素是运用定积分元素法解决具体问题的关键. 理解了积分元素的本质,就会避免实际应用中的随意性和盲目性,达到正确有效地选取积分元素的目的.积分元素，也称微元或元素，是定积分“化曲为直，以直代曲”思想的具体表现，是定积分应用中所谓“元素法”的核心的精华所在。寻求积分元素问题是用定积分解决实际问题的关键一步。定积分是微积分中的重要内容，而定积分元素法经常被用在解决许多实际问题，如利用定积分元素法去求解几何、物理甚至是经济方面的问题。在数学分析中，我们经常用定积分的元素法求旋转体体积，利用定积分元素法求解第一、二型曲面积分，被积函数是单变量函数或可化为单变量函数的函数，利用积分元素法，能将其直接化为定积分计算，这种简单的算法还可以推广到计算具有类似特征的三重积分。 关键词：定积分，元素法，简单应用，微分 Element method of definite integral and its application Abstract : Reasonable selection of integral element is the use of the definite integral element method to solve specific problems . The key to understand the essence of integral element, can avoid the practical application of the randomness and blindness, to properly select the integral element. Element of the integral, also known as the element or elements, is the definite integral for straight and curly, straight generation of song of the thought specific performance, is the application of definite integral in the so-called element of the core essence. Seeking integral element is integral to solve practical problems with the key step. A definite integral is an important content in the calculus, and definite integral element method is used to solve many practical problems, such as the use of the definite integral element method to solving geometric, physical and economic aspects. In mathematical analysis, we often use element method of definite integral calculating the volume of rotating object, using the definite integral element method for solving the first, the two type of integral, the integrand is a function of a single variable or as a function of a single variable function, using