Find The Average Value Of F Over The Given Rectangle.

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Find the average value of f over the given rectangle.
f (x, y) = x^2y,
R has vertices (-1, 0), (-1, 5), (1, 5), (1, 0)

Answer: 5/6

Explanation

Recall that the average value of the integral is obtained by dividing the integral of the function with the area we are integrating over. Since our area is a rectangle given with the segments: [-1, 1] x [0, 5] the area of the rectangle is equal to 2 * 5 = 10.

We calculate the integral:

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