2006 SMT/General Problems/Problem 14
Solution
Noticing that the first equation, 
is the equation of a disk of radius 
, and that the graph of 
is an odd function which will divide the circle into two regions; an upper and lower half of equal areas, the solution is half the area of the circle (The area of upper section the be specific as the question ask for 
which satisfy 
). ![\[\frac{\pi \cdot r^2}{2} = \frac{\pi \cdot (\pi)^2}{2} = \boxed{\frac{\pi^3}{2}}\]](http://latex.artofproblemsolving.com/1/d/c/1dcae45b803720eb6c78005714212e8ceadc696f.png)
