定积分及其应用摘 要定积分最开始是由于求面积和体积等实际问题而出现的。它的出现是人类不断认识世界和改变世界的一个侧面反应，从古希腊的阿基米德使用“穷竭法”，魏晋时期刘徽使用“割圆术”到牛顿莱布尼茨公式的订立都反映着定积分的不断发展和进步。定积分现在已经成为解决相关实际问题的有力工具，牛顿莱与布尼茨给出的计算定积分的方法使得原本相互独立的微分学和积分学联系在了一起，共同构成了现在完整的微积分学理论体系。定积分是函数的特定结构总和式的极限。这种极限不仅在数学方面有应用，在解决实际问题中也应用广泛，比如说运用定积分可以在经济学与物理学方面计算一些常见的问题。本论文主要讨论一些定积分的基本的概念、性质和方法继而引导出它在其他学科方面的运用。通过研究一些性质、运算方法和定理来解决实际应用问题。定积分性质主要有三个即：可加性、非负性、连续性。运算方法有换元积分法和分部积分法。关键字：定积分、性质、定理、应用AbstractThe definite integral begins with the actual problem of area and volume. The emergence of it is to know the world and change the world one side reaction, from the ancient Greek Archimedes used the method of exhaustion, Liu Hui wei-jin period using "cyclotomic surgery" Newton leibniz formula to conclude all reflects the definite integral of the continuous development and progress. Definite integral now has become a powerful tool to solve the actual problem, Newton, and cloth has given the calculation of the definite integral method makes the differential calculus and integral calculus of originally independent together, now constitute a complete system of calculus theory.The definite integral is the limit of the sum of the specific structures of the function. This limit is applied not only in mathematics, but also in solving practical problems, such as using definite integrals to calculate common problems in economics and physics. This paper mainly discusses the basic concepts, properties and methods of definit...
