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Find the total area of the region enclosed between the curves y = x² and y = sqrt(|x|).

1. 1/3
2. 2/3
3. 1/6
4. 1

Correct answer: 2/3

Solution

On each side the curves meet at x = 0 and x = 1; integrating (sqrt(x) - x²) gives 1/3 per side, so the total enclosed area is 2/3.

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