Determine the area of the region bounded by the curve y = 2x - x² and the x-axis. A. 2/3 B. 4/3 C. 1 D. 3/2 Answer: B) 4/3 Explanation: The curve intersects the x-axis at x = 0 and x = 2. Area = ∫[0 to 2] (2x - x²) dx = [x² - x³/3] from 0 to 2 = (4 - 8/3) - 0 = 4/3.

imo class 12 definite integration

Determine the area of the region bounded by the curve y = 2x - x² and the x-axis.

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Determine the area of the region bounded by the curve y = 2x - x² and the x-axis.

Answer: B) 4/3

Explanation: The curve intersects the x-axis at x = 0 and x = 2. Area = ∫[0 to 2] (2x - x²) dx = [x² - x³/3] from 0 to 2 = (4 - 8/3) - 0 = 4/3.