Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If _0^x 1-(f'(t))^2 dt=...

Question

Let f be a non-negative function in [0, 1] and twice differentiable in (0, 1). If _0^x 1-(f'(t))^2 dt= _0^xf(t)dt, 0 1 and f(0) = 0, then _ x 0 1 x^2 _0^xf(t)dt :

Accepted Answer

(D)

JEE Main 2021 Mathematics question

Solution