Show $\iint_{D} f(x,y)(1 - x^2 - y^2) ~dx ~dy = \pi/2$ Suppose $f(x,y)$ is a bounded harmonic function in the unit disk
$D = \{z = x + iy : |z| < 1 \} $
and $f(0,0) = 1$. Show that
$$\iint_{D} f(x,y)(1 - x^2 - y^2) ~dx ~dy = \frac{\pi}{2}.$$
I'm studying for a prelim this August and I haven't taken Complex in a long time (two years ago).  I don't know how to solve this problem or even where to look unless it's just a game with Green's theorem-any help?  I don't need a complete solution, just a helpful hint and I can work the rest out on my own.

Begin with the mean value property of harmonic functions:
$\int_0^{2 \pi} f(r \cos \theta, r \sin \theta) d\theta =f(0,0)  2 \pi $. 
