定积分线性换元法的教学研究  

The teaching study on linear substitutions of definite integrals

作　　者：于正文[1] 

机构地区：[1]山东建筑大学理学院,山东济南250101

出　　处：《山东建筑大学学报》2012年第2期255-258,共4页Journal of Shandong Jianzhu University

基　　金：山东省高等学校教学改革研究项目(2009262)

摘　　要：为了简化定积分的计算,提高计算效率,综合分析了定积分的各种计算方法,利用线性换元法推导出了一个新的定积分计算公式,并给出严格的证明。经多个例子的计算表明:此公式可以简单有效地解决某些由幂函数、指数函数与三角函数组合的定积分计算问题以及一些定积分恒等式证明问题,它为定积分的计算提供了一个新的简便实用的计算方法。Various computational methods of definite integrals are synthesized to simplify calculations of definite integrals and increase computational efficiency. An integral formula is derived by a linear substitution and is proved strictly in this paper. The computations by several examples show that by u- sing it and a linear substitution some integrals can be simply and efficiently calculated which are com- posed of power functions, exponential functions and trigonometric functions and some integral equali- ties can be proved. It provides a new simple and practical method to compute definite integrals

关 键 词：定积分 线性换元 积分公式 

分 类 号：O172[理学—数学]