The area enclosed by the curve y = eˣ, y = x, x = 0 and x = 1 is: A. (e − 3/2) sq units B. (e − 1) sq units C. (e − 1/2) sq units D. (e − 2) sq units Answer: A) (e − 3/2) sq units Explanation: Area = ∫[0 to 1] (eˣ − x) dx = [eˣ − x²/2]₀¹ = (e − 1/2) − (1 − 0) = e − 3/2 sq units.

imo class 12 application of integrals

The area enclosed by the curve y = eˣ, y = x, x = 0 and x = 1 is:

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The area enclosed by the curve y = eˣ, y = x, x = 0 and x = 1 is:

Answer: A) (e − 3/2) sq units

Explanation: Area = ∫[0 to 1] (eˣ − x) dx = [eˣ − x²/2]₀¹ = (e − 1/2) − (1 − 0) = e − 3/2 sq units.