The area enclosed by the parabola y² = 8x and the line y = 2x is:

The area enclosed by the parabola y² = 8x and the line y = 2x is:

• A. 4/3 sq units
• B. 2/3 sq units
• C. 8/3 sq units
• D. 16/3 sq units

Answer: A) 4/3 sq units

Explanation: Solving: (2x)² = 8x → 4x² = 8x → 4x(x − 2) = 0 → x = 0, 2. When x = 2, y = 4 (upper). Area = 2 × ∫[0 to 2] (√(8x) − 2x) dx (for y≥0, upper half then double). For y≥0: parabola y = √(8x), line y = 2x (for 0≤x≤2). Area above x-axis = ∫[0 to 2] (√(8x) − 2x) dx = [ (2√2)(2/3)x^(3/2) − x² ]₀² = (4√2/3)×2^(3/2) − 4 = (4√2/3)×(2√2) − 4 = (4×4/3) − 4 = 16/3 − 4 = 4/3. Total area = 2 × (4/3) = 8/3 sq units.