The Maximum Value of Integral Limit Function ∫x+ax∣sin t∣dt and Its Graph Inflection Point
A special kind of integral limit function f(x)=∫x+ax∣sin t∣dt is studied.Firstly,analyzed that the function f(x)is a periodic derivative function with a period of π.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.
integral limit functionmaximum valueinflection pointfundamental formulas of calculus
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