关于∫_(0)^(kπ/2)sin^(m)x·cos^(n)xdx型定积分解法探究  

Research on the Solution of Definite Integral of ∫_(0)^(kπ/2)sin^(m)x·cos^(n)xdx

作　　者：王晨龙 李丽霞[1] WANG Chenlong;LI Lixia(Bohai University,Jinzhou,Liaoning Province,121013 China)

机构地区：[1]渤海大学,辽宁锦州121013

出　　处：《科技资讯》2021年第21期192-195,共4页Science & Technology Information

摘　　要：定积分计算是数学分析和高等数学中的重要内容,也是学好其他知识必备的数学基础,因此该文首先对沃利斯公式,即:形如∫_(0)^(π/2)sin^(n)xdx和∫_(0)^(π/2)cos^(n)xdx形式定积分进行推广,得到形如∫_(0)^(kπ/2)sin^(m)x·cos^(n)xdx的定积分;然后,对其求解方法进行探究,得出其一般求解公式(定理1);最后,将积分区间由[0,π/2]推广到[0,kπ/2]及任意区间,得出4个推论,并通过例题对该方法进行应用。The calculation of definite integral is not only an important content in mathematical analysis and higher mathematics,but also a necessary mathematical basis for learning other knowledge well.Therefore,Wallis formula is generalized in this paper,I get a definite integral of type ∫_(0)^(kπ/2)sin^(m)x·cos^(n)xdx.Explore its solution method and obtain its general solution formula(Theorem 1).In the end,I’m going to generalize the interval from [0,π/2]to [0,kπ/2]and any interval.Four conclusions were drawn and an example is given to apply the method.

关 键 词：定积分 凑微分 三角函数 双阶乘 

分 类 号：O172.2[理学—数学]