Find the average value of f over the given rectangle. f(x, y) = 2x2y, r has vertices (−2, 0), (−2, 5), (2, 5), (2, 0).

average is 0

Step-by-step explanation:

I insert each x and y corresponding value into the f(x,y) equation and got:

0

40

-40

0

and then I found the average by adding them up and dividing but the amount of numbers:

0/4 = 0

This is kind of a strange answer so if you made a mistake writing something please message me and I can redo this problem.

If the expression is x^2 + y^2 = z, means that the radius is √z.

That is because the general expression of a circle with the center at the origin of the coordinate system is x^2 + y^2 = (radius)^2

Then in  your expression z = (radius)^2, and the radius is found by taking square root>

√(radius)^2  =  √z

=>radius = √z