Find the average value of f over region d. f(x, y) = 5xy, d is the triangle with vertices (0, 0), (1, 0), and (1, 8).

The average value of over the region is

We can describe the region as the set

So the integral in the numerator is

The integral in the denominator is the same as the area of , which is a right triangle, so it's easy to compute

So the average value is .