Calculate the area of the region bounded by the parabolas y = 2x² and y = x² + 4. A. 32/3 B. 16/3 C. 64/3 D. 8/3 Answer: A) 32/3 Explanation: Intersections: 2x² = x² + 4 → x² = 4 → x=±2. Area = ∫(−2 to 2) (x² + 4 − 2x²) dx = 2∫(0 to 2) (4 − x²) dx = 32/3 sq units.

imo class 12 application of integrals

Calculate the area of the region bounded by the parabolas y = 2x² and y = x² + 4.

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Calculate the area of the region bounded by the parabolas y = 2x² and y = x² + 4.

Answer: A) 32/3

Explanation: Intersections: 2x² = x² + 4 → x² = 4 → x=±2. Area = ∫(−2 to 2) (x² + 4 − 2x²) dx = 2∫(0 to 2) (4 − x²) dx = 32/3 sq units.