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Find the area (in square units) of the region {(x, y): x >= 0, x + y <= 3, x² <= 4y, y <= 1 + sqrt(x)}.

1. 5/2
2. 59/12
3. 3/2
4. 7/3

Correct answer: 59/12

Solution

The bounded region lies above the parabola x²/4 and below the upper envelope (the curve 1 + sqrt(x) up to x = 2, then the line 3 - x), giving total area 59/12.

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