I think I might be able to. All you want to do is graph the function, then find the upper and lower bounds of the integral, most likely wherever the function crosses/touches the x axis. By my calculations it looks like the lower bound will be 0, and the upper bound 2. Then, since this is a disk, all you need to do is take the square of the function when integrating, find that, and then since it is circular motion, tack on pi.
Hope this helps.