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.

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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.

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