一类定积分的Z变换计算方法

Solving a Class of Integrals with Z Transform

本文首次利用Z变换的方法来求解一类形如∫0πac o+s(bcnoxs)xdx和∫0πasi+n(bnsixn)xdx的定积分,其中n为非负整数参数,a,b为实数,并且得到了完整的积分公式。由此,我们可以直接获得数学分析中此类定积分的值。同时,Z变换的方法也同样适用于类似的含参变量的定积分的计算。

This paper calculates a class of definite integral such as ∫π0cos（nx）a＋bcosxdx and ∫π0sin（nx）a＋bsinxdx（n∈N,a,b∈R） by the method of Z transform for the first time,and the whole integrated formula is given.Thus,we can obtain the results of this class of definite integral in mathematics analysis directly.And,the method of Z Transform is suitable for the similar definite integral with parameter calculation.