对积分integral from n=0 to +∞((sinx/x)dx)的深入研究——兼论对偶与非对偶法则之比较

Thorough Research into Integral integral from n=0 to +∞((sinx/x)dx)——Concurrently discussing the antithesis to compare with the non-antithesis principle

对积分I=∫0^＋∞sinx/xdx=π/2的计算方法进行深入研究，从多种渠道得出这一结果，值得注意的是本文应用了Fourier积分变换的对偶性质，巧妙而不失优美地给出了一个新方法。

This article reseaches the calculating methods of the integral I =∫0^＋∞sinx/xdx=π/2 in various ways. It is notable that the antithesis nature of the fourier integral transformation is applied to the study, and a new convergent integral--∫0^＋∞sinx/xdx=π/2 comes out.