The area of the smaller region bounded by the circle x² + y² = 4 and the line x = 1 is:

The area of the smaller region bounded by the circle x² + y² = 4 and the line x = 1 is:

• A. (4π/3 − √3) sq units
• B. (2π/3 − √3) sq units
• C. (π/3 − √3) sq units
• D. (4π/3 + √3) sq units

Answer: A) (4π/3 − √3) sq units

Explanation: Region to the right of x = 1. Area = 2 × ∫[1 to 2] √(4 − x²) dx. Using ∫√(a²−x²) dx = (x/2)√(a²−x²) + (a²/2)sin⁻¹(x/a). Area = 2[(x/2)√(4−x²) + 2 sin⁻¹(x/2)]₁² = 2[0 + 2(π/2) − (1/2)√3 − 2(π/6)] = 2[π − √3/2 − π/3] = 2[2π/3 − √3/2] = 4π/3 − √3 sq units.