积分限函数∫_(x)^(x+a)|sin t|dt的最值及图形的拐点

The Maximum Value of Integral Limit Function ∫_(x)^(x+a)|sin t|dt and Its Graph Inflection Point

研究了一类特殊的积分限函数f(x)=∫_(x)^(x+a)|sin t|dt。首先分析得到函数f(x)是一个周期为π的周期可导函数,再利用微积分基本公式和积分限函数求导公式两种方法,分别研究函数f(x)的最值问题,然后利用拐点的判定方法得到曲线f(x)的拐点坐标,最后对此积分限函数进行推广,并利用MATLAB软件画图验证,旨在更深入地理解和掌握积分限函数的性态。

A special kind of integral limit function f(x)=∫_(x)^(x+a)|sin t|dt sin t dt is studied.Firstly,analyzed that the function f(x)is a periodic derivative function with a period ofπ.The problem of the maximum value of the func-tion f(x)is studied by the basic formula of calculus and the derivative formula of the integral limit function.Then,the inflection coordinates of the graph f(x)are obtained by the judgment method of the inflexion point.Finally,this integral limit function is generalized,and the MATLAB software is used to draw a diagram for verification.It aims to have a deeper understanding and grasp of the properties of the integral limit function.