Area bound by the parabola 2y = x² and the line x = y - 4 is equal to
- A. 4.5
- B. 9
- C. 18
- D. 36
Answer: C. 18
Explanation: Intersection: x = x²/2 - 4 => x² - 2x - 8 = 0 => (x-4)(x+2)=0. x = -2, 4. Area = Integral from -2 to 4 of (x+4) - (x²/2) dx. [x²/2 + 4x - x³/6] from -2 to 4. (8+16-64/6) - (2-8+8/6) = (24 - 10.67) - (-6 + 1.33) = 13.33 - (-4.67) = 18.