某些“积不出”函数的定积分近似计算方法及其原函数的近似曲线  

The Approximate Calculation Method and Curve of Some “Beyond Element” Definite Integrals

作　　者：杨立敏 王泽军 马鹏 于静 陈文 

机构地区：[1]中国石油大学(北京),克拉玛依校区,文理学院,新疆 克拉玛依

出　　处：《理论数学》2020年第7期631-637,共7页Pure Mathematics

摘　　要：通常所说的“求不定积分”是指用初等函数的形式把这个不定积分表示出来,如果函数的原函数不是初等函数,则称此函数为“积不出”函数。“积不出”函数的定积分计算时“Newton-Leibniz”公式失效。本文用无穷级数理论和含参变量积分理论给出部分“积不出”函数的定积分近似计算方法,用Matlab编程数值计算部分“积不出”函数的定积分近似值,并与讨论的其广义积分值加以比较,又利用变上限函数绘制了部分“积不出”函数的原函数近似曲线。In general, “Calculating definite integral” is that we show the definite integral using elementary function, whereas, if the primitive function is not elementary function, then definite integral is “Beyond Element”. At this point, the “Newton-Leibniz” formula can not apply to calculate “Beyond Element” definite integral. In this paper, we apply theory of infinite series and integral depending on a parameter to calculate some “Beyond Element” definite integral. We obtain approximate value of definite integral by applying Matlab of mathematical software, and compare with analytical result of generalized integral. Subsequently, we apply variable upper limit function to plot the ap-proximate curve of primitive function.

关 键 词：“积不出”函数 无穷级数 含参变量积分 MATLAB 近似曲线 

分 类 号：O17[理学—数学]