Integral

合集下载

matlab 积分函数

matlab 积分函数一、介绍在数学中，积分是求解函数面积、体积、曲线长度等问题的重要工具。

在MATLAB中，有很多内置的积分函数可以帮助我们进行数值积分。

本文将详细介绍MATLAB中的积分函数。

二、MATLAB中的基本积分函数1. quad函数quad函数是MATLAB中最常用的数值积分函数之一。

它可以用来计算单变量或多变量实值函数的定积分。

quad函数采用自适应辛普森公式进行计算，因此可以得到较高的精度。

quad函数的调用方式如下：I = quad(fun,a,b)其中fun是被积函数，a和b是定积分区间。

例如，要计算sin(x)在[0,pi]区间上的定积分，可以使用以下代码：fun = @(x) sin(x);a = 0;b = pi;I = quad(fun,a,b)2. integral函数integral函数也是MATLAB中常用的数值积分函数之一。

它使用自适应高斯-库恩公式进行计算，并且可以处理有限和无限区间上的定积分。

integral函数的调用方式如下：I = integral(fun,a,b)其中fun是被积函数，a和b是定积分区间。

例如，要计算exp(-x^2)在[-inf,inf]区间上的定积分，可以使用以下代码：fun = @(x) exp(-x.^2);a = -inf;b = inf;I = integral(fun,a,b)3. dblquad函数dblquad函数是MATLAB中用来计算二重积分的函数。

它采用自适应辛普森公式进行计算，并且可以处理有限区间和无限区间上的二重积分。

dblquad函数的调用方式如下：Q = dblquad(fun,xmin,xmax,ymin,ymax)其中fun是被积函数，xmin、xmax、ymin和ymax是二重积分区间。

例如，要计算f(x,y)=x^2+y^2在[0,1]×[0,1]区域内的二重积分，可以使用以下代码：fun = @(x,y) x.^2 + y.^2;xmin = 0;xmax = 1;ymin = 0;ymax = 1;Q = dblquad(fun,xmin,xmax,ymin,ymax)三、MATLAB中的高级积分函数除了基本的数值积分函数外，MATLAB还提供了一些高级的数值积分函数，可以处理更加复杂的问题。

integrative词根

integrative词根integrative词根 1.词根：inter, integr = 整, 全同源词：1. integral [integr整，全 + -al…的→]adj.完整的，整体的2. integrality [见上，-ity名词后缀→]n.完整性，完全3. integrity [integr整，全 + -ity名词后缀→]n.完整，完全，完善4. integrate [integr整，全 + -ate 动词后缀→]v.使结合成一整体，使并入，使一体化，结为一体;[使黑人与白人成为一体] (美国)取消种族隔离5. integration [见上，-ion名词后缀→]n.整体化，一体化，结合，综合，取消种族隔离6. integrative [见上，-ive…的→]adj. 一体化的，整体化的，综合的7. integrant [integr整→整体 + -ant表示物→]n.& adj. 构成整体的组成部分，要素，成份 ;[-ant…的] 构成整体的，成分的，要素的8. disintegrate [dis-取消，不 + integr整 + -ate 后缀→使不成为一个整体→]v. (使)瓦解，(使)9. disintegrator [见上，-or表示人或物]n.瓦解者，粉碎机10. redintegrate [red-再 + integr 整 + -ate 后缀→再成为一个整体→]v.使再完整11. integer [见上，-er 名词后缀→]n.整数，完整的东西2.词根：integr 整, 全integral [integr整，全，-al…的] 完整的，整体的integrality [见上，-ity名词后缀] 完整性，完全integrity [integr整，全，-ity名词后缀] 完整，完全，完善integrate [integr整，全，-ate动词后缀] 使结合成一整体，使并入，使一体化，结为一体;[使黑人与白人成为一体] (美国)取消种族隔离integration [见上，-ion名词后缀] 整体化，一体化，结合，综合，取消种族隔离integrative [见上，-ive…的] 一体化的，整体化的，综合的integrant [integr整→整体，-ant表示物] 构成整体的组成部分，要素，成份’[-ant…的] 构成整体的，成分的，要素的disintegrate [dis-取消，不，integrate结合] (使)瓦解，(使)分裂disintegrator [见上，-or表示人或物] 瓦解者，分裂者.粉碎机redintegrate [red-再，integrate成整体，完整] 使再完整integer 整数，完整的东西integrative的用法adj.综合的，一体化的;1. chinese ocean economy needs integrative management in rich ocean areas and resources.中国海洋经济的发展需要对海洋区域和丰富的海洋资源进行海洋综合管理.2. hence enacted law is more authoritative and more integrative than judge - made law.因此,制定法比法官造法更具有权威性和统一性.3. a new viewpoint of chemical - and - plant integrative fixation is put forward.提出了开展化学 - 生物一体化固沙新观点.4. integrative champion two races biaoyou club the fist special ring spring 2004.2004年北京飙友俱乐部春季第一届特比环双关综合冠军(黑马作出,王顺利使翔).5. chapter two: theoretical foundation and value analysis of chinese integrative learning.第二章语文综合性学习的理论基础和价值分析.6. the class of single chip madine is very integrative and pracficas.单片机是一门综合性和实践性很强的课程.7. in the course of its development, an integrative aggregative tension appeared.在教育政治学发展的过程中, 出现了两种张力:整合的张力和多元的张力.8. life and art are integrative.生活和艺术是一体的.9. based chain - linked model , it gives an improved technological innovation process model named as integrative model.提出了技术创新过程的整体观模型, 并结合彩电行业的案例分析,指出了其理论和现实意义.10. parallel - flow heat exchanger has the advantage of integrative performance considering the pressure drop, size and weight.从阻力性能, 体积和重量等综合方面考虑,平行流式换热器要优于翅片管式换热器.integrative的词汇搭配integrative trend 综合趋势integrative suppression 整合校正integrative approach 积分方法theory of integrative level 整合层次的理论..。

高数中英文专业名词对照

高数中英文专业名词对照以下是一些高等数学中的中英文专业名词对照：1.代数学(Algebra):●代数表达式(Algebraic Expression)●方程式(Equation)●多项式(Polynomial)●因式分解(Factorization)●线性方程组(System of Linear Equations)●不等式(Inequality)2.微积分学(Calculus):●导数(Derivative)●微分(Differentiation)●积分(Integral)●不定积分(Indefinite Integral)●定积分(Definite Integral)●微积分基本定理(Fundamental Theorem of Calculus)●微分方程(Differential Equation)3.解析几何学(Analytic Geometry):●平面坐标系(Cartesian Coordinate System)●直线方程(Equation of a Line)●圆方程(Equation of a Circle)●曲线方程(Equation of a Curve)●空间几何(Three-Dimensional Geometry)4.线性代数(Linear Algebra):●矩阵(Matrix)●行列式(Determinant)●特征值和特征向量(Eigenvalues and Eigenvectors)●向量空间(Vector Space)●线性变换(Linear Transformation)●内积和外积(Dot and Cross Products)5.概率论与数理统计(Probability and Mathematical Statistics):●概率(Probability)●随机变量(Random Variable)●概率分布(Probability Distribution)●期望值(Expectation)●方差(Variance)●统计推断(Statistical Inference)6.数学分析(Mathematical Analysis):●数列(Sequence)●级数(Series)●极限(Limit)●导数学(Differential Calculus)●积分学(Integral Calculus)●泰勒级数(Taylor Series)●傅里叶级数(Fourier Series)请注意，这些对照可能根据不同的教材和学科有所不同，而且在实际应用中，有时候专业术语的翻译也会因上下文而略有变化。

gre 同义词总结大全

gre 同义词总结大全GRE同义词总结大全GRE是美国研究生入学考试，考查考生的词汇量和逻辑推理能力。

在备考GRE时，词汇的积累是必不可少的，而词汇的复习中同义词的记忆也是一个重要的方面。

下面是GRE的一些常用词汇同义词总结，希望对你的备考有所帮助。

1. Accurate 准确的同义词：Precise、Exact、Correct、Right2. Challenge 挑战同义词：Difficulty、Obstacle、Problem、Dilemma3. Comprehend 理解同义词：Understand、Grasp、Follow、Cognize4. Diverse 多样的同义词：Varied、Different、Various、Heterogeneous5. Enhance 增强同义词：Improve、Strengthen、Boost、Elevate6. Evaluate 评估同义词：Assess、Appraise、Analyze、Judge7. Fundamental 基本的同义词：Basic、Essential、Crucial、Primary8. Global 全球的同义词：Worldwide、International、Universal、Globe-spanning9. Infer 推断同义词：Deduce、Conclude、Gather、Draw10. Innovative 创新的同义词：Original、Creative、Revolutionary、Inventive11. Objective 客观的同义词：Unbiased、Impartial、Fair、Neutral12. Perceive 察觉同义词：Notice、Detect、Sense、Recognize13. Reluctant 不情愿的同义词：Hesitant、Unwilling、Resistant、Unenthusiastic14. Resolve 解决同义词：Settle、Sort out、Tackle、Deal with15. Skeptical 怀疑的同义词：Doubtful、Cynical、Disbelieving、Unconvinced16. Strengthen 加强同义词：Reinforce、Intensify、Consolidate、Enhance17. Subsequent 随后的同义词：Following、Later、Next、Successive18. Suppress 镇压同义词：Repress、Quell、Quash、Crush19. Validate 验证同义词：Confirm、Check、Substantiate、Authenticate20. Accomplish 完成同义词：Achieve、Fulfill、Realize、Accomplish21. Analyze 分析同义词：Examine、Study、Investigate、Inspect22. Attribute 属性同义词：Quality、Characteristic、Trait、Feature23. Compose 组成同义词：Form、Constitute、Make up、Construct24. Decipher 破译同义词：Crack、Decode、解读、解码25. Decline 下降同义词：Dwindle、Diminish、Decrease、Fall26. Inevitable 不可避免的同义词：Unavoidable、Inescapable、Certain、Unpreventable27. Integral 不可或缺的同义词：Essential、Necessary、Fundamental、Critical28. Obsolete 过时的同义词：Outdated、Outmoded、Antiquated、Old-fashioned29. Prosperous 繁荣的同义词：Thriving、Successful、Flourishing、Prospering30. Redundant 多余的同义词：Excessive、Superfluous、Unnecessary、Surplus31. Reluctant 不情愿的同义词：Hesitant、Unwilling、Resistant、Unenthusiastic32. Renounce 放弃同义词：Abandon、Give up、Quit、Relinquish33. Sparse 稀疏的同义词：Scattered、Thinning、Limited、Sparse34. Suppress 镇压同义词：Repress、Quell、Quash、Crush35. Validity 有效性同义词：Credibility、Authenticity、Legitimacy、Soundness36. Virus 病毒同义词：Bacteria、Infection、Microorganism、Pathogen37. Yield 放弃同义词：Surrender、Relinquish、Cede、Give in以上是GRE常用的词汇同义词总结，需要大家在备考过程中反复记忆、使用和模仿。

matlab定积分函数

matlab定积分函数
在MATLAB中，可以使用`integral`函数来计算定积分。

`integral`函数的基本语法如下：
```matlab
Q = integral(fun,a,b)
```
其中，`fun`是被积函数的句柄，`a`和`b`是积分区间的下限和
上限。

`integral`函数将返回积分结果`Q`。

例如，计算函数 f(x) = x^2 在区间 [0,1] 上的定积分，可以按照以下方式使用`integral`函数：
```matlab
f = @(x) x^2;
a = 0;
b = 1;
Q = integral(f,a,b);
```
注意，被积函数`f`应当是一个标量函数或矢量函数，并且应当接受一个输入参数并返回一个输出值。

此外，`integral`函数还可以用于计算多重积分。

在这种情况下，`a`和`b`应当被定义为向量，分别表示每个维度上的积分区间
的下限和上限。

更多关于`integral`函数的详细信息可以通过在MATLAB命令窗口输入`help integral`命令来获取。

积分用英语怎么说

积分用英语怎么说商家为了刺激消费者消费，是一种变相营销的手段。

比如，满多少积分可换购某样商品。

积分获取的途径：购物，做任务，参加某种活动。

那么你知道积分用英语怎么说吗?下面来学习一下吧。

积分英语说法：integral积分的相关短语：不定积分indefinite integral ; antiderivative ; Primitive function ; indefinite integration数值积分 numerical integration ; Integration point ; Integral approximation ; numerical integral积分表lists of integrals ; Integration formulae ; Standard integral ; table of integral指数积分Exponential integral ; Expint ; Ei maple ; Well function黎曼积分 Riemann integral ; Riemann integrability ; riemann calculus ; Riemann Sums积分符号 integral symbol ; Integral sign ; Signs For Integrals ; Integralzeichen曲线积分line integral ; curvilinear integral ; Curved Line Integral积分时间Integral Time ; Integration time ; reset time ; Integrationszeit积分赛 Points Race ; tournament ; Score-O ; Ranked Match 积分的英语例句：1. He graduated with a GPA of 3.8.他毕业时各科成绩的平均积分点为3.8。

matlab数组积分

matlab数组积分Matlab是一种常用的科学计算软件，它提供了丰富的数学函数和工具包，可以方便地进行数值计算、数据分析和可视化等操作。

其中，数组积分是Matlab中常用的数值计算方法之一，可以用来求解函数的定积分。

本文将详细介绍Matlab中的数组积分方法及其应用。

在Matlab中，我们可以使用内置函数`integral`来进行数组积分。

该函数的基本语法如下：```Q = integral(fun,a,b)```其中，`fun`是要积分的函数句柄，`a`和`b`分别是积分区间的上下限。

通过调用`integral`函数，我们可以得到函数在给定区间上的定积分值`Q`。

在使用`integral`函数时，我们需要定义一个函数句柄来表示要积分的函数。

例如，如果我们要计算函数f(x)=x^2在区间[0,1]上的定积分，可以定义如下的函数句柄：```fun = @(x) x.^2```然后，我们可以调用`integral`函数进行积分计算：```Q = integral(fun,0,1)```通过这样的方式，我们可以方便地求解函数的定积分。

除了基本的数组积分方法外，Matlab还提供了其他一些常用的积分函数，如`quad`和`quadl`等。

这些函数可以用于求解一些特殊类型的积分，如数值积分、自适应积分等。

这些函数的使用方法与`integral`类似，只是在具体的参数设置上略有不同。

除了求解定积分外，Matlab还可以进行多重积分的计算。

对于多重积分，我们可以使用`integral2`、`integral3`等函数来实现。

这些函数的使用方法与`integral`相似，只是需要传入不同维度的积分区间和函数句柄。

通过这些函数，我们可以方便地求解多元函数的积分。

在实际应用中，数组积分在很多领域都有着广泛的应用。

例如，在工程领域，我们经常需要对信号进行分析和处理，而信号的能量谱密度可以通过对信号的幅度平方进行积分来获得。

Integral

IntegralFrom Wikipedia, the free encyclopediaThis article is about the concept of definite integrals in calculus. For the indefinite integral, see antiderivative. For the set of numbers, see integer. For other uses, see Integral (disambiguation).A definite integral of a function can be represented as the signed area of the region bounded by its graph.The integral is an important concept in mathematics. Integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function f of a realvariable x and an interval[a, b] of the real line, the definite integralis defined informally as the signed area of the region in the xy-plane that is bounded by the graph of f, the x-axis and the vertical lines x = a and x = b. The area above the x-axis adds to the total and that below the x-axis subtracts from the total.Roughly speaking, the operation of integration is the reverse of differentiation. For this reason, the term integral may also refer to the related notion of the antiderivative, a function F whose derivative is the given function f. In this case, it is called an indefinite integral and is written:The integrals discussed in this article are those termed definite integrals. It is the fundamental theorem of calculus that connects differentiation with the definite integral: if f is a continuousreal-valued function defined on a closed interval [a, b], then, once an antiderivative F of f is known, the definite integral of f over that interval is given byThe principles of integration were formulated independently by Isaac Newton and Gottfried Leibniz in the late 17th century, who thought of the integral as an infinite sum of rectangles of infinitesimal width. A rigorous mathematical definition of the integral was given by Bernhard Riemann. It is based on a limiting procedure which approximates the area of a curvilinear region by breaking the region into thin vertical slabs. Beginning in the nineteenth century, more sophisticated notions of integrals began to appear, where the type of the function as well as the domain over which the integration is performed has been generalised. A line integral is defined for functions of two or three variables, and the interval of integration [a, b] is replaced by a certain curve connecting two points on the plane or in the space. In a surface integral, the curve is replaced by a piece of a surface in the three-dimensional space.Integrals of differential forms play a fundamental role in modern differential geometry. These generalizations of integrals first arose from the needs of physics, and they play an important role in the formulation of many physical laws, notably those of electrodynamics. There are many modern concepts of integration, among these, the most common is based on the abstract mathematical theory known as Lebesgue integration, developed by Henri Lebesgue.Contents∙ 1 Historyo 1.1 Pre-calculus integrationo 1.2 Newton and Leibnizo 1.3 Formalizationo 1.4 Historical notation∙ 2 Terminology and notation∙ 3 Interpretations of the integral∙ 4 Formal definitionso 4.1 Riemann integralo 4.2 Lebesgue integralo 4.3 Other integrals∙ 5 Propertieso 5.1 Linearityo 5.2 Inequalitieso 5.3 Conventions∙ 6 Fundamental theorem of calculuso 6.1 Statements of theorems▪ 6.1.1 Fundamental theorem of calculus▪ 6.1.2 Second fundamental theorem of calculus ∙7 Extensionso7.1 Improper integralso7.2 Multiple integrationo7.3 Line integralso7.4 Surface integralso7.5 Integrals of differential formso7.6 Summations∙8 Computationo8.1 Analyticalo8.2 Symbolico8.3 Numericalo8.4 Mechanicalo8.5 Geometrical∙9 Some important definite integrals∙10 See also∙11 Notes∙12 References∙13 External linkso13.1 Online booksHistorySee also: History of calculusPre-calculus integrationThe first documented systematic technique capable of determining integrals is the method of exhaustion of the ancient Greek astronomer Eudoxus(ca.370 BC), which sought to find areas and volumes by breaking them up into an infinite number of divisions for which the area or volumewas known. This method was further developed and employed by Archimedes in the 3rd century BC and used to calculate areas for parabolas and an approximation to the area of a circle. Similar methods were independently developed in China around the 3rd century AD by Liu Hui, who used it to find the area of the circle. This method was later used in the 5th century by Chinese father-and-son mathematicians Zu Chongzhi and Zu Geng to find the volume of a sphere (Shea 2007; Katz 2004, pp. 125–126).The next significant advances in integral calculus did not begin to appear until the 16th century. At this time the work of Cavalieri with his method of Indivisibles, and work by Fermat, began to lay the foundations of modern calculus, with Cavalieri computing the integrals of x n up to degree n = 9 in Cavalieri's quadrature formula. Further steps were made in the early 17th century by Barrow and Torricelli, who provided the first hints of a connection between integration and differentiation. Barrow provided the first proof of the fundamental theorem of calculus. Wallis generalized Cavalieri's method, computing integrals of x to a general power, including negative powers and fractional powers.Newton and LeibnizThe major advance in integration came in the 17th century with the independent discovery of the fundamental theorem of calculus by Newton and Leibniz. The theorem demonstrates a connection between integration and differentiation. This connection, combined with the comparative ease of differentiation, can be exploited to calculate integrals. In particular, the fundamental theorem of calculus allows one to solve a much broader class of problems. Equal in importance is the comprehensive mathematical framework that both Newton and Leibniz developed. Given the name infinitesimal calculus, it allowed for precise analysis of functions within continuous domains. This framework eventually became modern calculus, whose notation for integrals is drawn directly from the work of Leibniz.FormalizationWhile Newton and Leibniz provided a systematic approach to integration, their work lacked a degree of rigour. Bishop Berkeley memorably attacked the vanishing increments used by Newton, calling them "ghosts of departed quantities". Calculus acquired a firmer footing with the development of limits. Integration was first rigorously formalized, using limits, by Riemann. Although all bounded piecewise continuous functions are Riemann integrable on a bounded interval, subsequently more general functionswere considered—particularly in the context of Fourier analysis—to which Riemann's definition does not apply, and Lebesgue formulated a different definition of integral, founded in measure theory (a subfield of real analysis). Other definitions of integral, extending Riemann's and Lebesgue's approaches, were proposed. These approaches based on the real number system are the ones most common today, but alternative approaches exist, such as a definition of integral as the standard part of an infinite Riemann sum, based on the hyperreal number system.Historical notationIsaac Newton used a small vertical bar above a variable to indicate integration, or placed the variable inside a box. The vertical bar was easily confused with .x or x′, which Newton used to indicate differentiation, and the box notation was difficult for printers to reproduce, so these notations were not widely adopted.The modern notation for the indefinite integral was introduced by Gottfried Leibniz in 1675 (Burton 1988, p. 359; Leibniz 1899, p. 154). He adapted the integral symbol, ∫, from the letter ſ (long s), standing for summa (written as ſumma; Latin for "sum" or "total"). The modern notation for the definite integral, with limits above and below the integral sign, was first used by Joseph Fourier in Mémoires of the French Academy around 1819–20, reprinted in his book of 1822 (Cajori 1929, pp. 249–250; Fourier 1822, §231).Terminology and notationThe simplest case, the integral with respect to x of a real-valued function f(x), is written asThe integral sign ∫ represents integration. The symbol dx (explained below) indicates the variable of integration, x. The function f(x) which is to be integrated is called the integrand. In correct mathematical typography, the dx is separated from the integrand by a space (as shown). Some authors use an upright d (that is, d x instead of dx). Also, some authors place the symbol dx before f(x) rather than after it. Because there is no domain specified, the above integral is called an indefinite integral.When integrating over a specified domain, we speak of a definite integral. Integrating over a domain D is written as . If D is an interval[a, b] of the real line, the integral is usually written . The domain D or the interval [a, b] is called the domain of integration. If a function has an integral, it is said to be integrable. In general,the integrand may be a function of more than one variable, and the domain of integration may be an area, volume, a higher-dimensional region, or even an abstract space that does not have a geometric structure in any usual sense (such as a sample space in probability theory).In modern Arabic mathematical notation, a reflected integral symbolis used (W3C 2006).The symbol dx has different interpretations depending on the theory being used. In Leibniz's notation, dx is interpreted as an infinitesimal change in x. Although Leibniz's interpretation lacks rigour, his integration notation is the most common one in use today. If the underlying theory of integration is not important, dx can be seen as strictly a notation indicating that x is a dummy variable of integration; if the integral is seen as a Riemann integral, dx indicates that the sum is over subintervals in the domain of x; in a Riemann–Stieltjes integral, it indicates the weight applied to a subinterval in the sum; in Lebesgue integration and its extensions, dx is a measure, a type of function which assigns sizes to sets; in non-standard analysis, it is an infinitesimal; and in the theory of differentiable manifolds, it is often a differential form, a quantity which assigns numbers to tangent vectors. Depending on the situation, the notation may vary slightly to capture the important features of the situation. For instance, when integrating a variable x with respect to a measure μ, the notation dμ(x) is sometimes used to emphasize the dependence on x.Interpretations of the integralIntegrals appear in many practical situations. If a swimming pool is rectangular with a flat bottom, then from its length, width, and depth we can easily determine the volume of water it can contain (to fill it), the area of its surface (to cover it), and the length of its edge (to rope it). But if it is oval with a rounded bottom, all of these quantities callfor integrals. Practical approximations may suffice for such trivial examples, but precision engineering (of any discipline) requires exact and rigorous values for these elements.Approximations to integral of √x from 0 to 1, with 5 ■ (yellow) right endpoint partitions and 12 ■ (green) left endpoint partitionsTo start off, consider the curve y = f(x) between x = 0 and x = 1 withf(xWhat is the area under the function f, in the interval from 0 to 1?and call this (yet unknown) area the (definite) integral of f. The notation for this integral will beAs a first approximation, look at the unit square given by the sides x = 0 to x = 1 and y = f(0) = 0 and y = f(1) = 1. Its area is exactly 1. As it is, the true value of the integral must be somewhat less than 1. Decreasing the width of the approximation rectangles and increasing the number of rectangles shall give a better result; so cross the interval in five steps, using the approximation points 0, 1/5, 2/5, and so on to 1. Fit a box for each step using the right end height of each curve piece,rectangles, we get a better approximation for the sought integral, namelyWe are taking a sum of finitely many function values of f, multiplied with the differences of two subsequent approximation points. We can easily see that the approximation is still too large. Using more steps produces a closer approximation, but will never be exact: replacing the 5 subintervals by twelve in the same way, but with the left end height of each piece, we will get an approximate value for the area of 0.6203, which is too small. The key idea is the transition from adding finitely many differences of approximation points multiplied by their respective function values to using infinitely many fine, or infinitesimal steps.As for the actual calculation of integrals, the fundamental theorem of calculus, due to Newton and Leibniz, is the fundamental link between the operations of differentiating and integrating. Applied to the square rootcurve, f(x) = x1/2, it says to look at the antiderivative F(x) = 3/2, andsimply take F(1) −F(0), where 0 and 1 are the boundaries of the interval [0, 1]. So the exact value of the area under the curve is computed formally as(This is a case of a general rule, that for f(x) = x q, with q≠ −1, the related function, the so-called antiderivative is F(x) = x q + 1/(q + 1).) The notationconceives the integral as a weighted sum, denoted by the elongated s, of function values, f(x), multiplied by infinitesimal step widths, theso-called differentials, denoted by dx. The multiplication sign is usually omitted.Historically, after the failure of early efforts to rigorously interpret infinitesimals, Riemann formally defined integrals as a limit of weighted sums, so that the dx suggested the limit of a difference (namely, the interval width). Shortcomings of Riemann's dependence on intervals and continuity motivated newer definitions, especially the Lebesgue integral, which is founded on an ability to extend the idea of "measure" in much more flexible ways. Thus the notationrefers to a weighted sum in which the function values are partitioned, with μmeasuring the weight to be assigned to each value. Here A denotes the region of integration.Differential geometry, with its "calculus on manifolds", gives the familiar notation yet another interpretation. Now f(x) and dx become a differential form, ω = f(x) dx, a new differential operator d, known as the exterior derivative is introduced, and the fundamental theorem becomes the more general Stokes' theorem,from which Green's theorem, the divergence theorem, and the fundamental theorem of calculus follow.More recently, infinitesimals have reappeared with rigor, through modern innovations such as non-standard analysis. Not only do these methods vindicate the intuitions of the pioneers; they also lead to new mathematics.Although there are differences between these conceptions of integral, there is considerable overlap. Thus, the area of the surface of the oval swimming pool can be handled as a geometric ellipse, a sum of infinitesimals, a Riemann integral, a Lebesgue integral, or as a manifold with a differential form. The calculated result will be the same for all.Darboux sumsDarboux upper sums of the function y = x2Darboux lower sums of the function y = x2Formal definitionsIntegral example with irregular partitions (largest marked in red)Riemann sums convergingThere are many ways of formally defining an integral, not all of which are equivalent. The differences exist mostly to deal with differing special cases which may not be integrable under other definitions, but also occasionally for pedagogical reasons. The most commonly used definitions of integral are Riemann integrals and Lebesgue integrals.Riemann integralMain article: Riemann integralThe Riemann integral is defined in terms of Riemann sums of functions with respect to tagged partitions of an interval.[1] Let [a, b] be a closed interval of the real line; then a tagged partition of [a, b] is a finite sequence, x i] indexed This partitions the interval [a, b] into n sub-intervals [x i−1by i, each of which is "tagged" with a distinguished point t i∈ [x i, x i].−1A Riemann sum of a function f with respect to such a tagged partition is defined asthus each term of the sum is the area of a rectangle with height equal to the function value at the distinguished point of the given sub-interval, and width the same as the sub-interval width. Let Δi= x i−x ibe the width−1of sub-interval i; then the mesh of such a tagged partition is the width of the largest sub-interval formed by the partition, max iΔi. The=1...nRiemann integral of a function f over the interval [a, b] is equal to S if:For all ε> 0 there exists δ> 0 such that, for any tagged partition [a, b] with mesh less than δ, we haveWhen the chosen tags give the maximum (respectively, minimum) value of each interval, the Riemann sum becomes an upper (respectively, lower) Darboux sum, suggesting the close connection between the Riemann integral and the Darboux integral.Lebesgue integralMain article: Lebesgue integrationRiemann–Darboux's integration (top) and Lebesgue integration (bottom)It is often of interest, both in theory and applications, to be able to pass to the limit under the integral. For instance, a sequence of functions can frequently be constructed that approximate, in a suitable sense, the solution to a problem. Then the integral of the solution function should be the limit of the integrals of the approximations. However, many functions that can be obtained as limits are not Riemann integrable, and so such limit theorems do not hold with the Riemann integral. Therefore, it is of great importance to have a definition of the integral that allows a wider class of functions to be integrated (Rudin 1987).Such an integral is the Lebesgue integral, that exploits the following fact to enlarge the class of integrable functions: if the values of a function are rearranged over the domain, the integral of a function should remain the same. Thus Henri Lebesgue introduced the integral bearing his name, explaining this integral thus in a letter to Paul Montel:I have to pay a certain sum, which I have collected in my pocket. I take the bills and coins out of my pocket and give them to the creditor in the order I find them until I have reached the total sum. This is the Riemann integral. But I can proceed differently. After I have taken all the money out of my pocket I order the bills and coins according to identical values and then I pay the several heaps one after the other to the creditor. This is my integral.Source: (Siegmund-Schultze 2008)As Folland (1984, p. 56) puts it, "To compute the Riemann integral of f, one partitions the domain [a, b] into subintervals", while in the Lebesgue integral, "one is in effect partitioning the range of f". The definition of the Lebesgue integral thus begins with a measure, μ. In the simplest case, the Lebesgue measureμ(A) of an interval A = [a, b] is its width, b−a, so that the Lebesgue integral agrees with the (proper) Riemann integral when both exist. In more complicated cases, the setsbeing measured can be highly fragmented, with no continuity and no resemblance to intervals.Using the "partitioning the range of f" philosophy, the integral of a non-negative function f:R→ R should be the sum over t of the areas between a thin horizontal strip between y = t and y = t + dt. This area is just μ{ x: f(x) >t} dt. Let f∗(t) = μ{ x: f(x) >t}. The Lebesgue integral of f is then defined by (Lieb& Loss 2001)where the integral on the right is an ordinary improper Riemann integral (f∗ is a strictly decreasing positive function, and therefore has a well-defined improper Riemann integral). For a suitable class of functions (the measurable functions) this defines the Lebesgue integral.A general measurable function f is Lebesgue integrable if the area between the graph of f and the x-axis is finite:In that case, the integral is, as in the Riemannian case, the difference between the area above the x-axis and the area below the x-axis:whereOther integralsAlthough the Riemann and Lebesgue integrals are the most widely used definitions of the integral, a number of others exist, including:∙The Darboux integral which is equivalent to a Riemann integral, meaning that a function is Darboux-integrable if and only if it is Riemann-integrable, and the values of the two integrals, if they exist, are equal. Darboux integrals have the advantage of being simpler to define than Riemann integrals.∙The Riemann–Stieltjes integral, an extension of the Riemann integral.∙The Lebesgue–Stieltjes integral, further developed by Johann Radon, which generalizes the Riemann–Stieltjes and Lebesgueintegrals.∙The Daniell integral, which subsumes the Lebesgue integral and Lebesgue–Stieltjes integral without the dependence on measures.∙The Haar integral, used for integration on locally compact topological groups, introduced by Alfréd Haar in 1933.∙The Henstock–Kurzweil integral, variously defined by Arnaud Denjoy, Oskar Perron, and (most elegantly, as the gauge integral) Jaroslav Kurzweil, and developed by Ralph Henstock.∙The Itō integral and Stratonovich integral, which define integration with respect to semimartingales such as Brownianmotion.∙The Young integral, which is a kind of Riemann–Stieltjes integral with respect to certain functions of unbounded variation.∙The rough path integral defined for functions equipped with some additional "rough path" structure, generalizing stochasticintegration against both semimartingales and processes such as the fractional Brownian motion.PropertiesLinearityThe collection of Riemann integrable functions on a closed interval [a, b] forms a vector space under the operations of pointwise addition and multiplication by a scalar, and the operation of integrationis a linear functional on this vector space. Thus, firstly, the collection of integrable functions is closed under taking linear combinations; and, secondly, the integral of a linear combination is the linear combination of the integrals,Similarly, the set of real-valued Lebesgue integrable functions on a given measure space E with measure μis closed under taking linear combinations and hence form a vector space, and the Lebesgue integralis a linear functional on this vector space, so thatMore generally, consider the vector space of all measurable functions on a measure space (E,μ), taking values in a locally compactcompletetopological vector space V over a locally compact topological field K, f: E→ V. Then one may define an abstract integration map assigning to each function f an element of V or the symbol ∞,that is compatible with linear combinations. In this situation the linearity holds for the subspace of functions whose integral is an element of V (i.e. "finite"). The most important special cases arise when K is R, C, or a finite extension of the field Q p of p-adic numbers, and V is a finite-dimensional vector space over K, and when K= C and V is a complex Hilbert space.Linearity, together with some natural continuity properties and normalisation for a certain class of "simple" functions, may be used to give an alternative definition of the integral. This is the approach of Daniell for the case of real-valued functions on a set X, generalized by Nicolas Bourbaki to functions with values in a locally compact topological vector space. See (Hildebrandt 1953) for an axiomatic characterisation of the integral.InequalitiesA number of general inequalities hold for Riemann-integrable functions defined on a closed and boundedinterval[a, b] and can be generalized to other notions of integral (Lebesgue and Daniell).∙Upper and lower bounds. An integrable function f on [a, b], is necessarily bounded on that interval. Thus there are real numbers m and M so that m≤ f (x) ≤ M for all x in [a, b]. Since the lower and upper sums of f over [a, b] are therefore bounded by,respectively, m(b−a) and M(b−a), it follows that∙Inequalities between functions. If f(x) ≤ g(x) for each x in [a, b] then each of the upper and lower sums of f is bounded above by the upper and lower sums, respectively, of g. ThusThis is a generalization of the above inequalities, as M(b−a) is the integral of the constant function with value M over [a, b].In addition, if the inequality between functions is strict, then the inequality between integrals is also strict. That is, if f(x) <g(x) for each x in [a, b], then∙Subintervals. If [c, d] is a subinterval of [a, b] and f(x) is non-negative for all x, then∙Products and absolute values of functions. If f and g are two functions then we may consider their pointwise products and powers, and absolute values:If f is Riemann-integrable on [a, b] then the same is true for |f|, andMoreover, if f and g are both Riemann-integrable then fg is also Riemann-integrable, andThis inequality, known as the Cauchy–Schwarz inequality, plays a prominent role in Hilbert space theory, where the left hand side is interpreted as the inner product of two square-integrablefunctions f and g on the interval [a, b].∙Hölder's inequality. Suppose that p and q are two real numbers, 1≤ p, q≤ ∞ with + = 1, and f and g are two Riemann-integrable functions. Then the functions |f|p and |g|q are also integrable and the following Hölder's inequality holds:For p = q= 2, Hölder's inequality becomes the Cauchy–Schwarzinequality.∙Minkowski inequality. Suppose that p≥ 1 is a real number a nd f and g are Riemann-integrable functions. Then | f |p, | g |p and |f +g |p are also Riemann integrable and the following Minkowskiinequality holds:An analogue of this inequality for Lebesgue integral is used in construction of L p spaces.ConventionsIn this section f is a real-valued Riemann-integrable function. The integralover an interval [a, b] is defined if a<b. This means that the upper and lower sums of the function f are evaluated on a partition a= x0≤ x1≤ . . . ≤ x n = b whose values x i are increasing. Geometrically, this signifies that integration takes place "left to right", evaluating f withinintervals [x i , x i +1] where an interval with a higher index lies to theright of one with a lower index. The values a and b, the end-points of the interval, are called the limits of integration of f. Integrals can also be defined if a>b:∙Reversing limits of integration. If a>b then defineThis, with a = b, implies:∙Integrals over intervals of length zero.If a is a real number thenThe first convention is necessary in consideration of taking integrals over subintervals of [a, b]; the second says that an integral taken over a degenerate interval, or a point, should be zero. One reason for the first convention is that the integrabilityof f on an interval [a, b] implies that f is integrable on any subinterval [c, d], but in particular integrals have the property that:∙Additivity of integration on intervals.If c is any element of [a, b], thenWith the first convention the resulting relationis then well-defined for any cyclic permutation of a, b, and c.Instead of viewing the above as conventions, one can also adopt the point of view that integration is performed of differential forms on oriented manifolds only. If M is such an oriented m-dimensional manifold, and M′ is the same manifold with opposed orientation and ω is an m-form, then one has:These conventions correspond to interpreting the integrand as a differential form, integrated over a chain. In measure theory, by contrast, one interprets the integrand as a function f with respect to a measure μand integrates over a subset A, without any notion of orientation; onewrites to indicate integration over a subset A. Thisis a minor distinction in one dimension, but becomes subtler onhigher-dimensional manifolds; see Differential form: Relation with measures for details.Fundamental theorem of calculusMain article: Fundamental theorem of calculusThe fundamental theorem of calculus is the statement that differentiation and integration are inverse operations: if a continuous function is first integrated and then differentiated, the original function is retrieved. An important consequence, sometimes called the second fundamental theorem of calculus, allows one to compute integrals by using an antiderivative of the function to be integrated.Statements of theoremsFundamental theorem of calculusLet f be a continuous real-valued function defined on a closed interval [a, b]. Let F be the function defined, for all x in [a, b], by。

influxdb的integral函数-概述说明以及解释

influxdb的integral函数-概述说明以及解释1.引言1.1 概述InfluxDB是一款开源的时间序列数据库，主要用于存储和处理时间序列数据。

其中的integral函数是InfluxDB的一个核心函数，用于计算时间序列数据在指定时间范围内的积分值。

积分值可以帮助我们更好地理解时间序列数据的趋势和变化情况，为数据分析和预测提供有力支持。

本文将详细介绍integral函数的原理和使用方法，以帮助读者更好地理解和应用这一功能。

同时，我们也将探讨integral函数在实际应用中的一些典型场景，希望能够为读者提供一些启发和思考。

通过学习和掌握integral函数，我们可以更好地利用InfluxDB的强大功能，发掘时间序列数据的潜力，为数据分析和决策提供更加可靠的支持。

1.2 文章结构：本文主要分为三个部分，分别为引言、正文和结论。

- 引言部分包括了对InfluxDB的简要介绍，以及文章的结构和目的。

- 正文部分将重点介绍integral函数的概念、原理和使用方法，让读者可以更加深入地了解这个函数。

- 结论部分将对integral函数进行总结，并探讨其在实际应用中的场景和未来的发展方向。

通过这三个部分的串联，读者可以系统地了解和学习关于influxdb的integral函数，从而更好地应用和利用这一功能。

1.3 目的本文旨在介绍InfluxDB中integral函数的基本概念和用法，以帮助读者更深入地了解这一函数在数据分析和处理中的作用。

通过对integral 函数的详细介绍，读者可以学习如何在InfluxDB中使用该函数来进行数据处理和计算，从而更好地应用它在实际项目中的场景中。

同时，通过对integral函数的使用方法进行讲解，读者可以在实际的数据分析和处理过程中灵活运用该函数，提高数据处理的效率和准确性。

最终，读者将能够更好地利用integral函数来分析和处理时序数据，以满足自己在数据处理领域的需求。

influxdb integral函数

influxdb integral函数
InfluxDB是一个开源的时间序列数据库，它提供了一组内置的函数来处理时间序列数据。

其中包括integral()函数用于计算时间序列数据的积分。

integral()函数可以用于计算在指定时间范围内的数据的累积值。

它的语法如下：
integral(column, [time])
参数说明：
column：要计算积分的字段名。

time：可选参数，指定时间范围，用于对数据进行聚合。

如果未提供时间参数，则会对所有数据进行积分。

示例用法：
SELECT integral(value) FROM measurement WHERE time >= '2022-01-01' AND time < '2022-01-02'
上述查询将计算在2022年1月1日至2022年1月2日期间的数据累积值，并返回结果。

integral()函数只能应用于数值型字段，而且在使用该函数之前，你需要确保数据已经按照时间顺序进行了排序。

matlab integral2 复杂函数积分

matlab integral2 复杂函数积分Matlab中的integral2函数用于求解二重积分，可以处理复杂的函数积分问题。

该函数的一般形式为：I = integral2(fun, xmin, xmax, ymin, ymax)其中fun是要求解的函数句柄，xmin和xmax是积分区间的x轴范围，ymin和ymax是积分区间的y轴范围。

integral2函数使用了自适应数值积分方法进行计算，可以在较高的精度下得到结果。

为了演示integral2函数的使用，我们将通过一个示例来说明。

假设我们要计算以下复杂函数的二重积分：f(x, y) = sin(x*y) / (x*y)^2在Matlab中，我们首先需要定义这个函数。

可以使用匿名函数的方式进行定义，代码如下：f = @(x, y) sin(x*y) ./ (x.*y).^2;接下来，我们可以使用integral2函数进行积分计算，代码如下：xmin = 0;xmax = pi;ymin = 0;ymax = pi;I = integral2(f, xmin, xmax, ymin, ymax);这里我们将积分区间设为[0, pi] x [0, pi]，通过调用integral2函数，得到求解结果。

下面我们将详细讲解integral2函数的工作原理和参数的含义。

1.自适应数值积分方法integral2函数使用了自适应数值积分方法进行计算。

该方法将积分区间分成多个小的区间，并对每个小区间进行数值积分计算。

如果某个小区间的计算误差超过指定的容差，那么该小区间会继续被划分成更小的子区间，直到达到指定的容差。

通过这种方法，可以在较高的精度下得到积分结果。

2.参数含义- fun：表示要求解的函数句柄。

该函数句柄可以是Matlab内置的函数，也可以是自己定义的函数。

在定义函数句柄时，可以使用Matlab提供的向量操作符和函数运算符。

另外，可以通过使用.操作符，对向量或矩阵中的每个元素进行操作。

particular integral数学含义

particular integral数学含义在差分方程、微分方程等数学问题中，特解特指一个解满足了给定的初始条件或边界条件。

这个特解被称为特解或者称为特定解（Integral solution）。

特解是一个具体的解，可以用来满足某些特定条件的问题。

在解微分方程的过程中，常常需要求解一个通解（General solution），它是微分方程的所有解的集合。

然后，为了满足特定的初值或边界条件，我们需要找到一个特解，以得到问题的完全解。

特解可以通过不同的方法求解。

以下是一些常见的方法和技巧：1. 齐次方程法：对于线性常系数齐次微分方程，我们可以先求解对应的齐次方程的解析解。

然后，通过假设特解形式的方法，找到一个特解。

2. 变量分离法：对于一些特殊形式的微分方程，可以通过变量分离法将方程转化为两个变量的乘积形式。

然后，通过积分求解得到特解。

3. 系数比较法：对于一些具有一定规律的微分方程，我们可以通过系数比较的方法求解特解。

通过对方程进行适当的变形和计算，得到特解。

4. 试解法：对于一些特定的微分方程，我们可以通过试解法来求解特解。

首先假设特解的形式，然后带入微分方程中，确定特解的形式和参数。

5. 奇偶性分析法：对于一些具有奇偶对称性的微分方程，我们可以通过奇偶性分析来求解特解。

通过对方程进行适当的变换和计算，得到特解。

特解的求解过程中，一般需要考虑方程的边界条件或者初值条件。

通过这些条件，可以确定一组特解或者取得通解中某个特定参数的值。

作为数学领域重要的概念之一，特解在科学研究、工程设计和应用数学等领域中扮演着重要的角色。

对于复杂的问题，特解的求解常常需要借助数值计算或者近似方法。

通过求解特解，我们可以得到问题的完整解析解，进一步了解问题的性质和规律。

在实际问题中，特解的求解是解决微分方程、差分方程等数学模型的关键一步。

它为我们理解和解决各种科学、工程和实际问题提供了有力的工具和手段。

matlab 数组积分

matlab 数组积分
在MATLAB 中，可以使用integral函数对数组进行积分。

该函数接受一个向量作为输入，并返回该向量的数值积分。

下面是一个示例，演示如何使用integral函数对数组进行积分：
matlab复制代码
% 创建一个向量
x = [0, 1, 2, 3, 4];
% 对向量 x 进行数值积分
result = integral(x, 0, 4);
% 输出结果
disp(result);
在上面的示例中，我们创建了一个包含 5 个元素的向量x，并使用integral函数对该向量进行数值积分。

integral函数的第一个参数是要积分的函数，这里我们传递x作为参数。

第二个参数是积分的起始值，这里设置为0。

第三个参数是积分的终止值，这里设置为4。

最后，我们将结果存储在变量result中，并使用disp函数将其输出。

注意，如果要对一个向量进行数值积分，可以将其视为一个函数，并在integral函数中传递该向量。

这样，MATLAB 将自动计算该向量的数值积分。

integral名词

integral名词
integral是一个英语单词，可以作为名词使用。

作为名词时，它的意思是：
1. 积分，整体，全体，完全的，完整的，集成的。

2. 积分，整数，整数部分。

3. 微分方程的解法。

4. 积分的部分，集成的部分。

、
integral是一个英语单词，可以作为形容词和名词使用。

作为形容词时，它的意思是“构成整体所必须的，不可缺的”，通常用来形容某个事物是整体中不可或缺的一部分。

例如，“Rice is an integral part of Chinese diet. 米饭是中餐中不可或缺的一部分。

”
作为名词时，它的意思是“整体，全体，完全，完整”，也可以指代积分、整数等数学概念。

integral的用法可以总结为以下几点：
1. 作为名词使用，表示整体、全体、完全、完整等概念。

2. 在数学领域中，integral可以指代积分或整数等概念。

Mathematics-积分（Integral）

Mathematics-积分（Integral）正⽂积分是微积分学与数学分析⾥的⼀个核⼼概念。

通常分为定积分和不定积分两种。

1 基本定义1.1 定积分对于⼀个给定的正实值函数f(x)，f(x) 在⼀个实数区间 [a,b] 上的定积分∫b a f(x)dx可以在数值上理解为在O xy坐标平⾯上，由曲线 (x,f(x))（x∈[a,b]），直线x=a，x=b以及X轴围成的曲边梯形的⾯积值（⼀种确定的实数值）。

其中的 d x称为积分变量，表⽰要求⾯积的范围是⽤坐标轴横轴的刻度计算；∫b a则表⽰从a开始算起，到b为⽌，称为积分范围或积分域，其中a称为积分下界，b称为积分上界，∫叫做积分号，是从拉长的字母S（拉丁⽂中的summa (ſumma)：求和的⾸字母）演变过来的。

函数f(x) 写在中间，称为被积函数。

1.2 不定积分f(x) 的不定积分（或原函数）是指任何满⾜导数是函数f(x) 的函数F(x)。

⼀个函数f(x) 的不定积分不是唯⼀的：只要F(x) 是f(x) 的不定积分，那么与之相差⼀个常数的函数F(x)+C也是f(x) 的不定积分。

⽆说明的情况下，下⽂中的“积分”⼀词均指“定积分”。

1.3 黎曼积分在实分析中，由黎曼创⽴的黎曼积分（英语：Riemann integral）⾸次对函数在给定区间上的积分给出了⼀个精确定义。

黎曼积分在技术上的某些不⾜之处可由后来的黎曼－斯蒂尔杰斯积分和勒贝格积分得到修补。

黎曼积分的基本概念就是对x-轴的分割越来越细，则其所对应的矩形⾯积和也会越来越趋近图形S的⾯积（如下图）。

1.3.1 区间的分割⼀个闭区间 [a,b] 的⼀个分割P是指在此区间中取⼀个有限的点列a=x0<x1<x2<…<x n=b。

每个闭区间 [x i,x i+1] 叫做⼀个⼦区间。

定义λ为这些⼦区间长度的最⼤值：λ=max，其中0\leq i\leq n-1。

⼀个闭区间[a,b]的⼀个取样分割是指在进⾏分割后，于每⼀个⼦区间中取出⼀点x_{i}\leq t_{i}\leq x_{i+1}。

inter词根的意思

inter词根的意思inter词根的意思 1.词根：inter, integr = 整, 全同源词：1. integral [integr整，全 + -al…的→]adj.完整的，整体的2. integrality [见上，-ity名词后缀→]n.完整性，完全3. integrity [integr整，全 + -ity名词后缀→]n.完整，完全，完善4. integrate [integr整，全 + -ate 动词后缀→]v.使结合成一整体，使并入，使一体化，结为一体;[使黑人与白人成为一体] (美国)取消种族隔离5. integration [见上，-ion名词后缀→]n.整体化，一体化，结合，综合，取消种族隔离6. integrative [见上，-ive…的→]adj. 一体化的，整体化的，综合的7. integrant [integr整→整体 + -ant表示物→]n.& adj. 构成整体的组成部分，要素，成份 ;[-ant…的] 构成整体的，成分的，要素的8. disintegrate [dis-取消，不 + integr整 + -ate 后缀→使不成为一个整体→]v. (使)瓦解，(使)9. disintegrator [见上，-or表示人或物]n.瓦解者，粉碎机10. redintegrate [red-再 + integr 整 + -ate 后缀→再成为一个整体→]v.使再完整11. integer [见上，-er 名词后缀→]n.整数，完整的东西2.词根：inter = whole, 表示“完整”integral a. 完整的(integr+al)integrity n. 完整，完全(integr+ity)integrate v. 使一体，使结合(integr+ate)disintegrate v. 使瓦解，分裂(dis分开+integr+ate→完整的分开→瓦解)disintegration n. 瓦解;分裂inter的前缀 1.前缀：inter-【词根含义】：中间,之间,相互【词根来源】：来源于拉丁语inter(之间,相互)。