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The area (in sq. units) of the region A = {(x, y): x² ≤ y ≤ x + 2} is:

1. 10/3
2. 9/2
3. 31/6
4. 13/6

Correct answer: 9/2

Solution

x^2=x+2 gives x=-1,2. Area=integral from -1 to 2 of (x+2-x^2) dx = 10/3-(-7/6) = 9/2.

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