I ran across a wonderful animation on Wikipedia that gave a perfect geometric interpretation about the process of multiple integration (in this case, double integrals). Therefore, I am wondering if something similar can be done in Mathematica, and if it can also be extended to triple integrals. If anyone could also provide the code, I would be very grateful.
This goes way beyond my skill level in Mathematica, therefore I would not even know where to start.
I found this that combined with the animation of the area sheets ($0$ to $ g(x,y)$), running from $x=a$ to $x=b$ and $y=f(a)$ to $y=f(b)$, could create the above animation. I think the hard part (at least for me) would be to create the animation of these sheets and synchronizing the movement with the segments in the x and y axis.
I found out that the above animation was created with Mathematica 9