[!] Calculus Help

I need help with this really soon, I’ve been puzzling over it for a while now, and I’ve got a project due tomorrow.

I’m trying to integrate the following equation:, depicted here: http://files.harishlall.com/cardioid.jpg (the one facing right is just the inverse).

I’ve just about determined that I can’t integrate it because it’s not a function (wishes that it wasn’t recursive). Now I’m trying to play with the cardioid in polar form, but does anyone know how to manipulate the polar equation for a cardioid to look something like that, and also do a 90 degree rotation. The cusp has to be on x=0 and it has to stretch to either x=6 or x=12.

Help, help, help!