The area of the smaller part of the circle x² + y² = a² cut off by the line x = a/√2 is:

The area of the smaller part of the circle x² + y² = a² cut off by the line x = a/√2 is:

• A. (a²/4)(π − 1) sq units
• B. (a²/4)(π/2 − 1) sq units
• C. (a²/2)(π/2 − 1) sq units
• D. (a²/2)(π − 1) sq units

Answer: A) (a²/4)(π − 1) sq units

Explanation: Smaller part is to the right of x = a/√2. Area = 2 ∫[a/√2 to a] √(a² − x²) dx = 2[(x/2)√(a²−x²) + (a²/2)sin⁻¹(x/a)]_(a/√2)^a = 2[0 + (a²/2)(π/2) − (a/(2√2))(a/√2) − (a²/2)(π/4)] = 2[a²π/4 − a²/4 − a²π/8] = 2[a²π/8 − a²/4] = a²π/4 − a²/2 = (a²/2)(π/2 − 1) sq units.