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Find the area of the region A = {(x, y): x² + y² <= 1 and y² <= 1 - x}.

1. pi/2 + 4/3
2. pi/2 - 4/3
3. pi/2 - 2/3
4. pi/2 + 2/3

Correct answer: pi/2 + 4/3

Solution

For -1 <= x <= 0 the circle bounds y; for 0 <= x <= 1 the parabola bounds y. Adding the left half-disc area pi/2 and the parabolic part 4/3 gives pi/2 + 4/3.

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