Let f be a non-negative function defined on the interval [0, 1]. If _0^x 1 - (f'(t))^2 ,dt = _0^xf(t) ,dt, 0 x 1, and f(0) = 0, then

JEE Advanced 2009 Mathematics question

Let f be a non-negative function defined on the interval [0, 1]. If

dt = f(t) dt, 0 x 1,

and f(0) = 0, then

Answer: (C)

Differentiating: , so . With f ≥ 0 and f(0) = 0, f must increase from 0: $ = 1 ⇒

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Question ID VK-037693