Let f: [0, 2] —> R be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0) = 1. Let F(x) = \int ^{x^2}_{0} f(\sqrtt) dt for x ∈ [0, 2].If F'(x) = f'(x) for all x ∈ (0, 2), then F(2) equals [JEE Adv 2014 P2]

Differentiation

Section: Mathematics

Question : 4 of 9

Marks: +1, -0

Let f: [0, 2] —> R be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0) = 1.
Let F(x) =

∫

f(√t)‌dt for x ∈ [0, 2].If F'(x) = f'(x) for all x ∈ (0, 2), then F(2) equals

[JEE Adv 2014 P2]

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