定积分的换元公式

Substitution formula for definite integrals

通过延拓变换函数的定义域,并使其保持连续的导函数性质,而其值域不变,证明了高等数学中定积分的一般换元公式,从而弥补了找不到其证明的缺憾。

By extending the domain of the transformation function such that it has still the same range as the original function, and continuous property of derivative function like the original function, this paper gives a proof of the general substitution rule for definite integrals. It makes up for the deficiency which its proof can not be found.