| 关于定积分近似计算中矩形法的误差估计 |
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| 引用本文： | 郑立飞,解小莉,王洁. 关于定积分近似计算中矩形法的误差估计[J]. 高等数学研究, 2011, 14(1): 5-6 |
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| 作者姓名： | 郑立飞 解小莉 王洁 |
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| 作者单位： | 西北农林科技大学应用数学系,陕西,杨凌,712100 |
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| 基金项目： | 西北农林科技大学教学改革项目 |
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| 摘 要： | 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.
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| 关 键 词： | 复合矩形法 分部积分法 拉格朗日中值定理 误差估计 |
Error Estimation of Approximating Definite Integrals by Rectangular Rule |
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| ZHENG Li-fei,XIE Xiao-li,WANG Jie. Error Estimation of Approximating Definite Integrals by Rectangular Rule[J]. Studies In College Mathematics, 2011, 14(1): 5-6 |
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| Authors: | ZHENG Li-fei XIE Xiao-li WANG Jie |
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| Affiliation: | (Applied Mathematical Department, Northwest A-F University, Yangling 712100, PRC) |
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| Abstract: | 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. |
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| Keywords: | Composite Rectangular Rule integration by parts Lagrange Mean ValueTheorem error estimation |
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