JEE Main 2024 Mathematics question
The area of the region enclosed by the parabolas y = 4x − x² and 3y = (x − 4)² is equal to
Answer: (D)
Solution
The parabolas meet at (1, 3) and (4, 0). Area = ∫₁⁴[(4x − x²) − (x − 4)²/3]dx = [2x² − x³/3 − (x − 4)³/9]₁⁴ = 32/3 − 14/3 = 6.