Calculate the area of the region bounded by the parabola y² = x and the straight line y = x. A. 1/6 B. 1/3 C. 1/2 D. 2/3 Answer: A) 1/6 Explanation: Intersections at x=0, x=1. Area = ∫(0 to 1) (√x − x) dx = [2/3 x^(3/2) − x²/2] = 2/3 − 1/2 = 1/6 sq units.

imo class 12 application of integrals

Calculate the area of the region bounded by the parabola y² = x and the straight line y = x.

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Calculate the area of the region bounded by the parabola y² = x and the straight line y = x.

Answer: A) 1/6

Explanation: Intersections at x=0, x=1. Area = ∫(0 to 1) (√x − x) dx = [2/3 x^(3/2) − x²/2] = 2/3 − 1/2 = 1/6 sq units.