Find the area of the region bounded by y = x³ and y = x in the first quadrant. A. 1/4 B. 1/2 C. 1/6 D. 1/3 Answer: A) 1/4 Explanation: Intersects at x=0, x=1. Area = ∫(0 to 1) (x − x³) dx = [x²/2 − x⁴/4] = 1/2 − 1/4 = 1/4 sq units.

imo class 12 application of integrals

Find the area of the region bounded by y = x³ and y = x in the first quadrant.

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Find the area of the region bounded by y = x³ and y = x in the first quadrant.

Answer: A) 1/4

Explanation: Intersects at x=0, x=1. Area = ∫(0 to 1) (x − x³) dx = [x²/2 − x⁴/4] = 1/2 − 1/4 = 1/4 sq units.