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The best way to Find the average value of f(x y) over the rectangle is to eliminate as many options as possible.

Find the average value of f over the given rectangle. f(x, y) = e^y \sqrt{x + e^y} , R = [0, 4] \times [0, 1]Watch the full video at:https://www.numerade.com

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Average value of f = 1 A ∫ ∫ R f (x, y) d A Where A is the area of the region R We can say: R = [− 1, 1] × [0, 5] Therefore A = 2 ⋅ 5 = 10 Average value of f = 1 10 ∫ − 1 1 [∫ 0 5 x 2 y d y] d x Integrate with

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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).

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