Find the average value of f over the given rectangle. f(x, y) = 3x2y, r has vertices (−5, 0), (−5, 3), (5, 3), (5, 0). g

We want to find the average value of f(x, y) on the given region.

The average value of f(x, y) in the given rectangle is 25.

So we want to find the average value of f(x, y) = 3*x^2*y on the rectangle with vertices (−5, 0), (−5, 3), (5, 3), (5, 0).

This will be given by the quotient between the integral of the function in that region and the area of the region, so we have:

Where we just solved the integral in the denominator, which just gives the area of the rectangle.

Now we need to solve the integral in the numerator, we can do it one variable at the time.

This means that the average value of f(x, y) in the given rectangle is 25.

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add the table and i will answer correctly

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