Asked • 04/14/24

Calculus 3 Double Integral Problem

Evaluate the integral ∫∫xydA in the first quadrant region bounded by y=x^2, y=x^3, y=5, and y=7.

Round your answer to 2 decimal places.

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Yefim S. answered • 04/15/24

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5 ≤ y ≤ 7; y1/3 ≤ x ≤ y1/2. ∫∫xydA = ∫57ydy ∫y^1/3y^1/2xdx = ∫57yx2/2y^1/3y^1/2dy = 1/2 ∫57y(y - y2/3)dy =

1/2(y3/3 - 3/8y8/3)57 = (73/6 - 3·78/3/16) - (53/6 - 3·58/3/16) = 16.4198

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Misha F.

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Unfortunately according to Lumen, that is not the answer. It says the answer is 36.33. Not sure how they got that. Thank you for trying. I have spent nearly 90 minutes trying variously ways to derive their answer. All mine are roughly the same as yours - nearly 1/2 their solution.
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04/15/24

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