Which do you think will be larger, the average value of (x, y) xy over the square 0 x 1, 0 y 1, or the average value of over the quarter circle x 2 y 2 1 in the first quadrant Calculate them to find out

Question: Which do you think will be larger, the average value of (x, y) = xy over the square 0 x 1, 0

Which do you think will be larger, the average value of ƒ(x, y) = xy over the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, or the average value of ƒ over the quarter circle x² + y² ≤ 1 in the first quadrant? Calculate them to find out.

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