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The area of the region described by A = {(x, y): x² + y² ≤ 1 and y² ≤ 1 − x} is:
- π/2 + 2/3
- π/2 + 4/3
- π/2 − 4/3
- π/2 − 2/3
Correct answer: π/2 + 4/3
Solution
The area is determined by the intersection of the unit circle and the parabola, which creates a bounded region. The area of the circular segment contributes π/2, while the area under the parabola adds an additional 4/3, leading to the total area of π/2 + 4/3.
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