integrals
简明释义
[数]积分
完整（integral 的复数）
英英释义
单词用法
积分部分；整数部份；主要的部分 | |
积分方程 |
同义词
反义词
| 导数 | The derivative of a function gives the rate of change at a specific point. | 一个函数的导数给出了特定点的变化率。 | |
| 离散的 | In discrete mathematics, we often deal with distinct and separate values. | 在离散数学中，我们通常处理的是不同和分开的值。 |
例句
1.The advantage of this method is you don't have to write any integrals.
这种方法的优点是，不用写出任何积分。
2.What if I add all of the small line integrals?
那如果将所有线积分都加起来呢？
3.In a few weeks, we will be triple integrals.
几个星期后，我们会学习三重积分。
4.I mean, you are doing single integrals.
我的意思是，做一元积分时。
5.You don't have to set up all these line integrals.
不用建立这些线积分。
6.So, in fact, I have to break this into two different integrals.
实际上，要拆成两个不同的积分。
7.Let's start right away with line integrals in space.
现在开始学习空间线积分了。
8.Other kinds of integrals we have seen are triple integrals.
我们学过的另一种积分是三重积分。
9.So, line integrals we know how to evaluate.
我们知道如何计算线积分。
10.The integrals 积分 of a function can be used to find the total distance traveled over time.
一个函数的 积分 integrals 可以用来计算随时间总共行驶的距离。
11.In calculus, we often study the properties of integrals 积分 to understand area under curves.
在微积分中，我们常常研究 积分 integrals 的性质，以理解曲线下的面积。
12.The area between two curves can be determined using integrals 积分 in definite form.
两个曲线之间的面积可以通过使用定积分的 积分 integrals 来确定。
13.In engineering, integrals 积分 are essential for analyzing load distribution on structures.
在工程学中，积分 integrals 对于分析结构上的载荷分布至关重要。
14.To solve this physics problem, we need to calculate the integrals 积分 of the velocity function.
要解决这个物理问题，我们需要计算速度函数的 积分 integrals。
作文
The concept of integrals is fundamental in the field of mathematics, particularly in calculus. An integral can be thought of as a way to calculate the area under a curve or the accumulation of quantities over a given interval. Understanding integrals is crucial for solving many real-world problems, from physics to engineering and even economics. To grasp the idea of integrals, we first need to understand its relationship with derivatives. While derivatives give us the rate of change of a function, integrals provide us with the total accumulation of that change over a specific range. For example, if we have a function that describes the speed of a car over time, the integral of that function would give us the total distance traveled by the car during that time period.There are two main types of integrals: definite and indefinite. A definite integral calculates the accumulation of a quantity between two specific limits, while an indefinite integral represents a family of functions and includes a constant of integration. The Fundamental Theorem of Calculus beautifully connects these two concepts, stating that differentiation and integration are inverse processes. This means that if you take the integral of a function and then differentiate the result, you will return to the original function.In practical applications, integrals can be used to determine areas, volumes, and even probabilities. For instance, in physics, when calculating the work done by a force, one often needs to compute the integral of the force function over a certain distance. Similarly, in economics, integrals can be used to find consumer and producer surplus, which are essential for understanding market dynamics.Moreover, the computation of integrals has been greatly facilitated by technology. With the advent of graphing calculators and computer software, it is now possible to evaluate complex integrals that would have been tedious to solve by hand. Numerical methods, such as the trapezoidal rule and Simpson's rule, allow us to approximate integrals even when an analytic solution is difficult to find.In conclusion, integrals are a powerful tool in mathematics that enable us to analyze and solve various problems across different fields. By mastering the concept of integrals, one can unlock a deeper understanding of the relationships between functions and their rates of change. Whether you are a student, a professional, or simply someone interested in the world around you, appreciating the significance of integrals will undoubtedly enhance your analytical skills and problem-solving abilities. As we continue to explore the vast landscape of mathematics, integrals will remain a cornerstone of our understanding, guiding us through the complexities of the universe.
在数学领域，特别是在微积分中，integrals（积分）的概念是基础。integral（积分）可以被视为计算曲线下方的面积或在给定区间内数量累积的一种方式。理解integrals对于解决许多现实世界的问题至关重要，从物理到工程甚至经济学。为了掌握integrals的概念，我们首先需要理解它与导数之间的关系。导数给我们提供一个函数的变化率，而integrals则提供了在特定范围内这种变化的总累积。例如，如果我们有一个描述汽车速度随时间变化的函数，那么该函数的integral（积分）将给出汽车在该时间段内行驶的总距离。Integrals主要有两种类型：定积分和不定积分。定积分计算在两个特定限制之间的数量累积，而不定积分表示一类函数，并包含一个积分常数。微积分基本定理巧妙地将这两个概念连接起来，指出微分和integrals是逆过程。这意味着如果你对一个函数进行integral（积分），然后对结果进行微分，你将返回到原始函数。在实际应用中，integrals可用于确定面积、体积甚至概率。例如，在物理学中，当计算力所做的功时，人们通常需要计算力函数在某个距离上的integral（积分）。同样，在经济学中，integrals可用于找出消费者和生产者剩余，这对于理解市场动态至关重要。此外，随着技术的发展，计算integrals变得更加容易。随着图形计算器和计算机软件的出现，现在可以评估复杂的integrals，即使手动求解也会很繁琐。数值方法，如梯形法则和辛普森法则，使我们能够近似计算integrals，即使在难以找到解析解的情况下。总之，integrals是数学中的一种强大工具，使我们能够分析和解决不同领域的各种问题。通过掌握integrals的概念，人们可以深入理解函数及其变化率之间的关系。无论你是学生、专业人士，还是仅仅对周围世界感兴趣的人，欣赏integrals的重要性无疑会增强你的分析能力和解决问题的能力。在我们继续探索广阔的数学领域时，integrals将始终是我们理解的基石，引导我们穿越宇宙的复杂性。
