本文利用定积分的性质、微分中值定理、施瓦兹不等式、二重积分等内容，研究了积分不等式的四种证法。
This article explores the four ways for solving integral inequality with the nature of definite integral, mean value theorem of differentials, Schwarz inequality and double integral.
在证明了定积分不等式等性质的基础上，给出并证明了积分中值定理的中值在开区间内取得的结论。
Based on the integral inequality and other quality proved, the paper discusses the conclusion of the mid-value in theorem of integration mean which is got in open interval.
文章研究了第一型曲线积分中值定理“中间点”的渐近性，获得了一些重要结果，得出它也是定积分中值定理相应结果的推广。
This paper discusses the asymptotic property of the Mid-point of the mean theorem for first form curvilinear integral.
文章研究了第一型曲线积分中值定理“中间点”的渐近性，获得了一些重要结果，得出它也是定积分中值定理相应结果的推广。
This paper discusses the asymptotic property of the Mid-point of the mean theorem for first form curvilinear integral.
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