关于Riemann积分分部积分公式的推广

A Generalization of Integration By Parts

本文利用和差变换公式,对分部积分公式进行了推广,得到函数u(x),v(x)在区间[a,b]上可导且b!au(x)dv(x)存在的条件下分部积分公式仍然成立,并结合数学分析教材中所给出的可积函数类,得到相应的两个推论.

This paper, by using the formula of sum-subtraction transform , improves the formula of integration by parts to get the integration by parts to further establish under the condition that derivable function u（x）,v（x） in the interval [a, b]and the integral ∫a^bu（x）dv（x） still exist. Combined with integrable function given in mathematics analysis two correspond-ing inferences are oblained.