Question

求高手翻译一段论文摘要，急需。。。非常感谢

在求一些函数的定积分时，由于原函数十分复杂难以求出或用初等函数表达，导致积分很难精确求出，只能设法求其近似值，因此能够直接借助牛顿-莱布尼兹公式计算定积分的情形是不多的。数值积分就是解决此类问题的一种行之有效的方法。积分的数值计算是数值分析的一个重要分支；因此，探讨近似计算的数值积分方法是有着明显的实际意义的。本文从数值积分问题的产生出发，详细介绍了一些数值积分的重要方法。
本文较详细地介绍了牛顿-科特斯求积公式，以及为了提高积分计算精度的高精度数值积分公式，即龙贝格求积公式和高斯-勒让德求积公式。除了研究这些数值积分算法的理论外，本文还将这些数值积分算法在计算机上通过matlab软件编程实现，并通过实例用各种求积公式进行运算，分析比较了各种求积公式的计算误差。

Answer 1

For some in the definite integral function, because the consequences are very complex difficult to find out or with elementary function expression, it is difficult to accurately find out in integral, can only try to ask the approximate, so can directly with newton-leibniz formula calculation of the definite integral situation is not much. Numerical integral to solve this kind of problem is an effective method. Integral numerical calculation of numerical analysis is an important branch; Therefore, to discuss the approximate calculation numerical methods is a obvious practical significance. This paper, from the start of the problem of numerical integration, detailed introduces some of the important methods of numerical integration.
The paper introduced in detail the Newton-for product formula, Kurt, and in order to improve the precision of the high precise numerical integral formulas, namely the dragon berger for product formula and gaussian-le let's ask product formula. In addition to research these numerical integral algorithm the theory, this paper will also these numerical algorithm in computer software programming realize through matlab, and through example for integrated with all kinds of formulas for computing, analyses and compares the various for product formula calculation error.

Answer 2

At the request of the definite integral of some function , the original function is very complex and difficult to find the elementary function expression , the integral is difficult to accurately calculate , only managed to find the approximate value , and allows direct interface with the Newton - Leibniz formula the case of the definite integral is small . Numerical integration is an effective method to solve such problems . The numerical integration is an important branch of numerical analysis ; therefore, explore the approximate calculation of the numerical integration method has obvious practical significance . Departure from the numerical integration problem , described in detail some of the numerical integration method .
This paper has detailed description of the Newton - Coates quadrature formula , and in order to improve the precision of the integral calculation accuracy of numerical integration formulas , Romberg quadrature formulas and the Gauss - Legendre quadrature formula . In addition to the study of these numerical integration algorithm theory , the article also compares these numerical integration algorithm by matlab program on your computer , and an example quadrature formula with a variety of operations, analysis and comparison of various quadrature formula calculation error .