Cotes求积公式截断误差的一种证明

A Kind of Proving Method for Truncation Error of Cotes Integral Formula

Cotes求积公式因具有较好的精度和稳定性而被广泛使用，但对其截断误差尚没有严格的推理过程。通过综合运用Newton插值公式、积分上限函数、分部积分以及积分中值定理等相关知识，推导出了Cotes求积公式的截断误差。

Cotes integral formula is widely used because of its good accuracy and stability, but there is still no strict derivation process to its truncation error. Through an integrated use of related knowledge about Newton interpolation formula, integral upper limit function, branch points and the mean value theorem, the error in Cotes integral formula is derived out.