The idea of the average value of a function, discussed earlier for functions of the form y = f (x), can be extended to functions of more than one independent variable. For a function z = f (x, y), he average value of f over a region R is defined as

where A is the area of the region R. Find the average value for each function over the regions R having the given boundaries.

ƒ(x, y) = e^2x+y; 1 ≤ x ≤ 2, 2 ≤ y ≤ 3

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[] f (x, y) dx dy, R A