Area Under Differentiable Function (Jee Mains)

Definite Integration Properties

Medium

Area Under Differentiable Function

Let ƒ : R→R be a twice differentiable function such that ƒ(x + y) = ƒ(x) ƒ(y) for all x, y ∈ R.
If ƒ'(0) = 4a and ƒ staisfies ƒ''(x) – 3a ƒ'(x) – ƒ(x) = 0, a > 0, then the area of the region
R = {(x,y) | 0 ≤ y ≤ ƒ(ax), 0 ≤ x ≤ 2} is :

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