基于中间点的渐近性质，获得了数值积分的校正公式及其条件误差估计。

Then Based on the asymptotic properties of the intermediate point, corrective formulas of numerical integral and its conditional errors are obtained.

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对于定积分近似计算中常使用的经典SIMPSON求积公式介绍一种新的简洁的证明方法并给出误差的最佳估计。

We introduced a new and simple proof of the classical SIMPSON quadrature formula which is frequently applied in calculating definite integrals and best estimation of error is obtained.

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