The area bounded by the curve x² = 4y and the line x = 4y − 2 is:

The area bounded by the curve x² = 4y and the line x = 4y − 2 is:

• A. 9/8 sq units
• B. 7/8 sq units
• C. 5/8 sq units
• D. 9/4 sq units

Answer: A) 9/8 sq units

Explanation: Solving: x² = 4y and x = 4y − 2 → y = x²/4. Substitute: x = 4(x²/4) − 2 = x² − 2 → x² − x − 2 = 0 → (x−2)(x+1) = 0 → x = −1, 2. Area = ∫[−1 to 2] ((x+2)/4 − x²/4) dx = (1/4) ∫[−1 to 2] (x + 2 − x²) dx = (1/4)[x²/2 + 2x − x³/3]₋₁² = (1/4)[(2+4−8/3) − (1/2−2+1/3)] = (1/4)[10/3 − (−7/6)] = (1/4)[20/6 + 7/6] = (1/4)(27/6) = 27/24 = 9/8 sq units.