关于积分中值定理的一个问题

A question on the mean value theorem of integral

在原有的积分中值定理的基础上加强了被积函数的条件得出了至少存在一点属于开区间的结论,给出了证明,并应用到形如lim∫1a xn/(1+x)(n→∞)这一问题的证明中。

Strengthened the integrand condition in the original integral theorem of mean＇s foundation to obtain has had a spot ξ belong to the open-interval （a,b） conclusion are given to prove, and applied shape like this limn→∞∫1a xn/1＋x dx=0（0≤a〈1） question in the proof, that was more effective.