关于定积分近似计算中矩形法的误差估计

Error Estimation of Approximating Definite Integrals by Rectangular Rule

利用拉格朗日中值定理给出复合矩形法的误差估计,并指出复合矩形法只有在等分的次数很大的时候才能比较精确的估计所求定积分的值.最后,给出复合矩形法、复合梯形法及复合抛物线法的误差估计实例.

This paper mainly used Lagrange Mean Value Theorem to formulate an error estimation of approximating definite integrals by rectangular rule. It indicates that the Composite Rectangular Rule yields better results if and only if the interval is partitioned into sufficient many small intervals. An example is used to compare the errors generated, respectively, by the composite rectangular, trapezoidal and parabolic rules.