关于|sinnx/sinx|~k定积分问题的探讨

The Discussion of the Definite Integral | Sinnx/Sinx |~k

本文根据定积分的性质和一些常用不等式对被积函数中含|sinnx/sinx|^k的这类定积分进行了研究,并对以其为通项的级数的敛散性进行了讨论,从而得到了级数敛散性和k的关系,为解决这类积分的问题提供了切实可行的解题方法。

The definite integral containing|sinnx/sinx|^k is discussed in this paper,and the convergence and divergence of the series as the general term according to the properties of the definite integral and some common inequalities.The relations are obtained between the series convergence and k,practical research methods are provided to solve this kind of integral problems.