Visualizing Double Integrals

For beginners, Double Integrals can be difficult to visualize as the resulting diagram is in 3 dimensions. Here are some resources that can help:

1) YouTube Animation

This excellent animation explains the concept behind double integration and also polar integrals.

2) Wolfram Alpha Command: 3dplot

This command can help to visualize the surface . For example, in Tutorial 7 Q3, what does the surface looks like?

You can type “3dplot z=x” into WolframAlpha: http://www.wolframalpha.com/input/?i=3dplot+z%3Dx

Result:

This makes sense, since means , i.e. we can see that the surface should be a plane.