你们都知道，要求这个面积是非常简单的，如果你们想的话，可以积分除了椭圆函数以外的任何函数。
So, you know, if you find that the area is too easy, you can integrate any function other than ellipse, if you prefer.
那么，你会说那很简单，积分就可以了，除非你不知道函数是什么。
So, you'd say, oh, it's easy. Let's just integrate, except you don't have a function.
垂直简单的意思是,在其中建立的对z积分会比较简单。
OK, so vertically simple means it will be something which I can setup an integral over the z variable first easily.
但是你知道，它给了你一个例证，其中你可以，把复杂的线积分化成简单些的二重积分。
But, you know, it gives you an example where you can turn are really hard line integral into an easier double integral.
先看看简单些的曲线的情形，这样我们解决二重积分会简单许多。
So maybe we first want to look at curves that are simpler, that will actually allow us to set up the double integral easily.
但我不知道有别的更简单的方法没，除了翻阅笔记中的积分表。
So, but I don't know any simpler solution except for one simpler solution, which is you have a table of integrals of this form inside the notes.
这是一个非常，简单的微分方程，两边积分。
Namely, this is still a pretty straightforward differential equation. So let's just integrate both sides.
这可能是周四考试的考点，如果周四考试遇到此类问题，在做了变量替换之后，积分边界变得很简单的。
So, probably the one that will be there on Thursday, if there's a problem about that on Thursday, it will be a situation where the bounds that you get after changing variables are reasonably easy.
一旦你开始学习代数，四则运算看起来就很简单了。当你学到微积分，四则运算简直就是小儿科。
Arithmetic looks easy once you start with algebra, which seems trivial once you go onto calculus.
相对简单的、找出边界的办法,就是在u、v坐标系下画出积分区域。
And to find the bounds perhaps the easiest is to draw a picture of a region in u, v coordinates.
最后，旨在实现了由简单的积分使用反射式准直激光视力和整体目标模块。
Finally, simplicity of aiming was achieved by use of integral reflex type collimating sight and integral laser aiming module.
将概率的基本思想，应用在计算实无穷积分中，结果表明该方法与小圆弧引理相比，计算更为方便简单、适用范围更为广泛。
To apply the basic idea of probability to the computing of real infinite integrals, to find that this method is more simple, convenient and widely used than the Small Arc Lemma.
本文就积分第一中值定理给出了一个简单的证明。
This paper gives a simple proof of the first mid -value theorem of Integral.
该控制器结构简单，易于实现，且不依赖对象数学模型，所包含的积分环节能有效观测并抑制对象中存在的不确定性。
The PID controller has a simple structure and doesn't rely on the math model, the integral action included observes and restrains the uncertainties of the plant.
以能量原理为基础，推导出变截面压杆计算临界力的简便方法，把复杂的积分运算归结为一个简单的代数运算。
Based on energy theory, a simple critical force calculation for pressed beam with variable cross sections is derived. It reduces the complex integration algorithm into a simple algebraic operation.
游戏的规则非常简单，通过连接4个相同颜色的方块到一起以获得积分。
The rules are simple, you get points by connecting 4 squares of the same color together.
基于积分法的动态数据校正具有简单、快速和适于在线应用的优点。
The integral method for dynamic data reconciliation has the advantages of simple and fitting online use over other methods.
本文从现代控制理论出发，利用状态空间法，与积分调节相结合，提出了一个简单实用的控制算法。
In this paper, based on the state space method of the modern control theory as well as the integral regulation, a simple and practical control algorithm was proposed.
提出了一种计算宽光谱间隔的普朗克函数积分值的简单近似方法。
A simple approximate method for calculating the values of integration of the Planck function over broad spectral intervals is presented.
通过计算两个简单的积分值，可近似表示菲涅耳单缝衍射的相对光强。
The relative intensity of Fresnel single-silt diffraction can be expressed approximately by means of two simpler integrals.
对切应变主轴不变的平面简单切变过程，通过无穷小应变的积分，导出了真实切应变计算公式。
An equation for the calculation of true shear strain was derived from the integration of infinitesimal shear strain in plane shearing process with constant principal shear strain direction.
对于层状模型，若采用直接积分的中心差分方法，计算过程十分简单，也可用于有限差分等方法的计算中。
For a layered model the computational procedure for the central difference method of direct integration is very simple and easy.
针对积分过程，提出了一种简单、实用的PID控制器。
It proposes a simple and effective PID controller for integrating processes.
文章用初等积分法直接来求其特解，该方法简单、方便，且适用范围广。
This article directly get it's special solution by the method of elementary integrals, and the method is simple and has wider range.
对积分时滞过程提出一种非线性比例控制算法，该算法只有一个可调参数，简单且实现容易。
A novel nonlinear proportion control algorithm is proposed for integrator processes with dominant time-delay. The algorithm has one parameter, so it is simple and realizes easily.
为了方便对会员信息的管理，提供更加简单，方便的操作平台，而设计了POS积分管理系统。
In order to facilitate the management of member information, provide a more simple and convenient platform, design the IMPS (Integration management of POS System).
为了方便对会员信息的管理，提供更加简单，方便的操作平台，而设计了POS积分管理系统。
In order to facilitate the management of member information, provide a more simple and convenient platform, design the IMPS (Integration management of POS System).
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