Find the average value of the function f(x, y) = 7/ x2 + y2 on the annular region a2 ≤ x2 + y2 ≤ b2, where 0 < a <
b.

Denote the annular region by . The average value of over is given by



For both integrals, convert the region to polar coordinates. We have








and so the average value is