Find the area of the region defined by the set {(x, y) : x² + y² ≤ 1 and x + y ≥ 1}.
Find the area of the region defined by the set {(x, y) : x² + y² ≤ 1 and x + y ≥ 1}.
- A. π/4 − 1/2
- B. π/2 − 1
- C. π/4 + 1/2
- D. π/4 − 1
Answer: A) π/4 − 1/2
Explanation: The region is inside the unit circle's first quadrant but above the line x+y=1. Area = (Area of quarter circle) − (Area of triangle) = π/4 − (1/2 × 1 × 1) = π/4 − 1/2.
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