Calculate the area bounded by the curves y = eˣ, y = e⁻ˣ, and the line x = 1. A. e + 1/e − 2 B. e − 1/e C. e + 1/e D. e − 1/e + 2 Answer: A) e + 1/e − 2 Explanation: Curves intersect at x=0. Area = ∫(0 to 1) (eˣ − e⁻ˣ) dx = [eˣ + e⁻ˣ] from 0 to 1 = (e + 1/e) − (1 + 1) = e + 1/e − 2 sq units.

imo class 12 application of integrals

Calculate the area bounded by the curves y = eˣ, y = e⁻ˣ, and the line x = 1.

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Calculate the area bounded by the curves y = eˣ, y = e⁻ˣ, and the line x = 1.

Answer: A) e + 1/e − 2

Explanation: Curves intersect at x=0. Area = ∫(0 to 1) (eˣ − e⁻ˣ) dx = [eˣ + e⁻ˣ] from 0 to 1 = (e + 1/e) − (1 + 1) = e + 1/e − 2 sq units.