Determine the area of the region bounded by the curve y = x² and the line y = 4. A. 32/3 B. 16/3 C. 8/3 D. 64/3 Answer: A) 32/3 Explanation: Intersections at x=−2, x=2. Area = ∫(−2 to 2) (4 − x²) dx = 2(4x − x³/3) from 0 to 2 = 2(8 − 8/3) = 32/3 sq units.

imo class 12 application of integrals

Determine the area of the region bounded by the curve y = x² and the line y = 4.

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Determine the area of the region bounded by the curve y = x² and the line y = 4.

Answer: A) 32/3

Explanation: Intersections at x=−2, x=2. Area = ∫(−2 to 2) (4 − x²) dx = 2(4x − x³/3) from 0 to 2 = 2(8 − 8/3) = 32/3 sq units.