区域R的面积是函数1在R上的二重积分。

The area R is the double integral over R of a function one.

youdao

求S上zdxdy的二重积分。

We will end up with double integral on S of z dxdy.

youdao

二重积分可以用来得到关于这个区域的某些信息，或者这个区域上的一个函数的平均值，等等。

We can use that to get information about maybe the region or about the average value of a function in that region and so on.

youdao

实际上，我们对二重积分的定义并不严谨，那应该怎样严格地定义它呢？

OK, so actually, how do we define it, that's not really much of a definition yet.

youdao

事实上，可以把求导放在积分里面。

So, we can actually move the derivatives into the integral.

youdao

在这里，是三维区域上的积分。

Here, you integrate over a three-dimensional region.

youdao

实际上，要拆成两个不同的积分。

So, in fact, I have to break this into two different integrals.

youdao

这就变成了C上的积分。

That will just become the integral over C.

youdao

好吧，微积分实际上是相当容易的。

Well calculus is actually pretty easy.

youdao

好吧，微积分实际上是相当容易的。

Well, calculus is actually pretty easy.

youdao

从精神上讲，带着没有扩大两队积分差距的成绩回家非常重要。

Mentally, to go home with the difference between the sides no wider is very important.

youdao

但是联赛也对于我们非常重要，因为我们想在积分榜上反弹到一个更好的位置上。

But the championship is very important for us too because we want to come back into a better position in the table.

youdao

但是联赛也对于我们非常重要，因为我们想在积分榜上反弹到一个更好的位置上。

But the championship is very important for us too because we want to come back into a better position in the table.

youdao