中文摘要：

综述了第一和第二积分中值定理的中值点在区间内部取得的改进定理，得到了一个简单的改进的积分第二中值定理．利用改进的第一和第二积分中值定理，对文献[1]中的一个典型题目给出了一题多解．

英文摘要：

The modified first and second mean value integral theorems that the mean value can be obtained in open interval are reviewed and a new modified second mean value integral theorem is obtained. Utilizing the modified first and second mean value integral theorems, multi-solutions of a classic mathematic problem in reference [1] are given.