对于剩下的愿意忍受我的人，我们继续，现在我们需要积分。
For the rest of you who are willing to bear with me, let's continue. So now let's just integrate.
我们需要计算通量的积分。
但在大多数情况下，我们需要了解怎样建立二重积分。
But most of the time we need to learn how to set up double integrals.
我们的这个太空游戏的主要目标是杀掉外星人并积分，所以我们需要一个过程来更改分数。
The main goal of our groovy space game is to kill aliens and accumulate points, so we'll need a procedure to alter the score.
了解这两种表述后，我们不仅需要向量场，就是左边这里，这是曲线c上的线积分，向量场在曲线上有定义。
So, in both cases, we need the vector field to be defined not only, I mean, the left hand side makes sense if a vector field is just defined on the curve because it's just a line integral on c.
这就是问题所在，如果你想积分，我们需要它处处有定义，旋度是0，那么你的积分也是。
OK, so that's the problem. I mean, if you try to integrate, we've said everywhere where it's defined, 0 the curl is zero. So, what you would be integrating would be zero.
但之后我们会用很酷的方法解决它，以及多元微积分，但目前，我们只需要写到这就行了，我们还不懂如何计算它。
However, we'll see one later using a cool trick, and multi-variable calculus. So, for now, we'll just leave the formula like that, and we don't know how long it is.
那么我们只需要知道，线积分正是势函数值的变化。
Then, we just have to, well, the line integral is just the change in value of a potential.
我们需要开始赢得积分。
现在我们需要做的就是尽可能多的去赢得积分。
那么我们将不会建立带上下限的积分，和积分dx,dy, dy, dx或者在极坐标做线积分，需要说，让我们回忆一下质心的定义。
So, instead of setting up the integral with bounds and integrating dx dy or dy dx or in polar coordinates, I'm just going to say, well, let's remember the definition of a center of mass.
现在切尔西和利物浦的状态都很纠结，所以我们面对他们的时候能获得积分也是很有希望的，但我们最需要的是以一场主场胜利来开头。
Chelsea and Liverpool have both been struggling a bit, so hopefully we'll pick up points against them, but we need to start with a home win.
我们需要取得全部积分，这意味着从比赛一开始就要发起进攻。
"We need to score full points which means a big attack from the start," said Brynildsen.
但是我们根本不去看那个积分榜，我们需要完全的把精力集中在下一场比赛，当然，我们在对法兰克福的比赛中收获了很多的自信。
But we shouldn't look at the table too often. We need to focus on the next match completely. We gained the right amount of self-esteem in Frankfurt for that.
该升+升曲轴箱是为积分气瓶，所以我们需要的东西的，以螺杆圆柱上曲轴箱。
The L+L crankcase is made for integral cylinders so we need something's to screw the cylinder onto the crankcase.
球队需要在联赛中度过几个愉快的星期，我们要争取很多积分，我希望这一切从下周的博尔顿开始。
We just need a couple of good weeks in the Premier League where we get a lot of points, and hopefully we can start next week against Bolton.
这个周末比赛有点困难，但至少我们拿到了一些积分。我们需要在下一站比赛有更好的结果。
The weekend was a little bit difficult but at least we got some good points and we need to get a better weekend at the next race.
我们的新的PCAP触摸屏不再需要制造商寻找既触摸屏的供应商和积分器到屏幕与显示器集成在一起。
Our new PCAP touchscreens eliminate the need for manufacturers to find both a touchscreen supplier and an integrator to integrate the screen with the display.
是关于复化梯形积分的程序，在这里我们可以实现对你需要的梯形求面积。
Minute of trapezoidal integration of the procedure, here we can achieve right you...
如同对数反三角函数功能整合需要一个主题通常讲授微积分第二，所以我们不会被他们融入这个类。
As with logarithms integrating inverse trig functions requires a topic usually taught in Calculus II and so we won't be integrating them in this class.
结合对数，通常需要一个教微积分第二，所以我们不会被集成在这个类对数的话题。
Integrating logarithms requires a topic that is usually taught in Calculus II and so we won't be integrating a logarithm in this class.
我们还需要一些积分，从这个周日开始，我们要尽可能在联赛中取得好成绩。
We still need a few points and we'll try to get them starting on Sunday.
我们还需要一些积分，从这个周日开始，我们要尽可能在联赛中取得好成绩。
We still need a few points and we'll try to get them starting on Sunday. We want to finish the league as well as possible.
昨天的胜利使得我们在联盟杯小组积分位居榜首。我们还需要努力，因为路还很长，表现良好也是十分必要的。
With yesterday's victory we are on top of our Uefa Cup group, we have to continue working well because the road ahead is still long and it's important for us to continue doing well.
昨天的胜利使得我们在联盟杯小组积分位居榜首。我们还需要努力，因为路还很长，表现良好也是十分必要的。
With yesterday's victory we are on top of our Uefa Cup group, we have to continue working well because the road ahead is still long and it's important for us to continue doing well.
应用推荐