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Find the area (in square units) of the region A = {(x, y): 0 <= y <= x*|x| + 1 and -1 <= x <= 1}.

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

Correct answer: 2

Solution

Integrating the upper boundary y = x|x| + 1 from -1 to 1, the odd part x|x| integrates to zero, leaving the integral of 1 over a length-2 interval, so the area is 2.

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