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Find the area (in square units) bounded by the parabola x² = 8y and the line x - 2y + 8 = 0.
- 36
- 72
- 18
- 9
Correct answer: 36
Solution
Intersection: x² - 4x - 32 = 0 => (x-8)(x+4) = 0 => x = -4 and x = 8. Area = integral₋₄⁸ [(x+8)/2 - x²/8] dx. Antiderivative: x²/4 + 4x - x³/24. At x=8: 16+32-512/24 = 48 - 64/3 = 80/3. At x=-4: 4-16+64/24 = -12+8/3 = -28/3. Area = 80/3 + 28/3 = 108/3 = 36.
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