You may learn the full details of Fubini's Theorem in an analysis course, but as an introduction to double integrals, you really needn't worry about it. For most, if not all, the function you deal with in practice, …

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Double integrals do more than find volume under three-dimensional graphs. Here we cover other uses, a more general notation for double integrals, and explain the "feel" of double integration.

Let's evaluate the double integrals with y=x^2 as one of the boundaries. Created by Sal Khan.

A double integral is just one regular integral inside of another. Thus, you can use integration techniques on the inside integral, then use integration techniques for the outside integral.

You hopefully have a little intuition now on what a double integral is or how we go about figuring out the volume under a surface. So let's actually compute it and I think it'll all become a lot more concrete.

The integrals will cancel out along all the cuts inside R itself. This is because for any cut, one of the integrals will go along it in one direction, while another goes along it in the other direction. In the end, …

If you have a two-variable function described using polar coordinates, how do you compute its double integral?

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Make sure you have a solid grasp of double integrals before reading through this. The main difficulty in understanding multiple integrals is going from the concept of single integration, to that of double …