Discussion
The average value of \( f(x,y) \) over a region \( R \) of area \( A \) is
Answer: A
As in one dimension, the average is the total divided by the extent over which it is spread:
\[ \bar{f} \;=\; \frac{1}{A}\iint_{R} f\,dA, \qquad A \;=\; \iint_{R} dA. \]
A constant integrand then returns its own value, which is the test any averaging formula must pass. The version with \( f^{2} \) leads to a root-mean-square instead
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