A partition of the interval [0,1] into n equal subdivisions gives

And endpoints

Similarly,

And

Since the function f(x,y)=8-2x-4y is decreasing in both variables, the minimum value of f(x,y) on the square

Is

In calculating the lower approximation sum, we will make use of the formula

With m_jk as in (1) and

The lower aproximation double sum is

Evaluating the limit as n goes to infinity of this approximating sum, we conclude that

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