中文摘要：

根据函数在端点和中点的泰勒展式,给出矩形求积公式的余项表达式,再根据余项表达式在某一点的固定值进行适当的修改,得到改进的左矩形、右矩形和中矩形求积公式.泰勒展式阶数越高,得到的改进矩形求积公式的代数精确度越高.再由改进的矩形求积公式得到改进梯形求积公式.最后用数值算例进行验证.

英文摘要：

By using Taylor’s formula for function at the end point and middle point,a kind of remainder term formula about the rectangular quadrature formula of the numerical integral formula can be obtained.Based on the fixed value of the remainder formula at a certain point,proper modification is made and the improved quadrature formula for left,right and middle rectangle is worked out.The higher the order of the Taylor’s formula is,the higher of the algebraic accuracy of the improved rectangular quadrature formula will be.The improved trapezium quadrature formula is then obtained through the improved rectangular quadrature formula.And the computational example is conducted to prove its validity.