Find the area of the region bounded by the parabola x² = 4y and the straight line x = 4y − 2. A. 9/8 B. 9/4 C. 3/8 D. 5/8 Answer: A) 9/8 Explanation: Substitute y = (x+2)/4 into parabola: x² = x+2 → x²−x−2=0. Roots x=−1, 2. Area = ∫(−1 to 2) ((x+2)/4 − x²/4) dx = 1/4 [x²/2 + 2x − x³/3] from −1 to 2 = 9/8 sq units.

imo class 12 application of integrals

Find the area of the region bounded by the parabola x² = 4y and the straight line x = 4y − 2.

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Find the area of the region bounded by the parabola x² = 4y and the straight line x = 4y − 2.

A. 9/8
B. 9/4
C. 3/8
D. 5/8

Answer: A) 9/8

Explanation: Substitute y = (x+2)/4 into parabola: x² = x+2 → x²−x−2=0. Roots x=−1, 2. Area = ∫(−1 to 2) ((x+2)/4 − x²/4) dx = 1/4 [x²/2 + 2x − x³/3] from −1 to 2 = 9/8 sq units.

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