That is what a double integral means.
这也就是二重积分的意义。
But let's do it as a double integral.
但是让我们用二重积分来做。
Now, how do we compute that double integral?
那么，怎么计算这个二重积分呢？
How do you express the area as a double integral?
如何用二重积分来表示面积呢？
We will end up with double integral on S of z dxdy.
求S上zdxdy的二重积分。
This side here is a usual double integral in the plane.
这边是平面上普通的二重积分。
You know how to compute a double integral of a function.
要懂得如何计算一个函数的二重积分。
Now I have everything I need to compute my double integral.
至此我已经得到了，用来计算二重积分的所有量。
The area R is the double integral over R of a function one.
区域R的面积是函数1在R上的二重积分。
We've seen various formulas for how to set up the double integral.
我们已经学过，如何建立这种二重积分的公式。
Use geometry or you need to set up for double integral of a surface.
总之，就是用几何方法或是在曲面上建立二重积分。
The double integral side does not even have any kind of renaming to do.
没有必要对二重积分重新命名了。
Because a surface is a two-dimensional object, that will end up being a double integral.
由于表面是二维的，所以结果是二重积分。
Because a surface is a two-dimensional object, that will end up being a double integral.
由于表面是二维的，所以结果是二重积分。
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