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Find the area of the region enclosed between the curves x = y² - 1 and x = |y| sqrt(1 - y²).

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

Correct answer: 2

Solution

By y-symmetry, integrate (right curve x = y sqrt(1-y²)) minus (left curve x = y² - 1) over y in [0,1] and double, giving total area 2.

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