The applet on this page is designed for experimenting with cartesian integration (as opposed to polar) in two dimensions.

It allows you to enter an integrand, and up to three boundary curves. These are entered in implicit form: If you want the region inside the unit circle, x2+y2 = 1, to be one of the boundary constraints, enter 1-(x^2+y^2) for a(x,y). The applet selects those points where a(x,y) >0 for the region of integration. If this is the only constraint you want, set b(x,y) =1, since then b(x,y)>0 is true at all points. There are instructions for how to enter other functions into these applets, but probably you should just try to enter things in and experiment -- always use * for multiplication, and ^ for powers, and make reasonable guesses about function names, and you may not need the instructions.

Also, when you click to go to the integration panel, click again after you get there. For reason unbeknownst to me, the canvas on which the integration info and such is reported erases itself after being drawn in. But a second click brings it back. The second click makes the exact same graphics calls, so this shouldn't happen. In any case, a second click cures it. If you know how to solve this -- the source is available on-line -- please let me know.

The applets take a while to load -- they are built out of a lot of building blocks of code, and do lots of things. But once downloaded, at least if you're going to do the project, there is a lot to do with them.