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Let f be a non-negative function defined...

Let `f` be a non-negative function defined on the interval `[0,1]`. If `int_0^xsqrt(1-(f^(prime)(t))^2)dt=int_0^xf(t)dt ,0lt=xlt=1,a n d \ f(0)=0`, then

A

`f((1)/(2))lt (1)/(2)` and `f((1)/(3))gt (1)/(3)`

B

`f((1)/(2))gt (1)/(2)` and `f((1)/(3))gt (1)/(3)`

C

`f((1)/(2))lt (1)/(2)` and `f((1)/(3))lt (1)/(3)`

D

`f((1)/(2))gt (1)/(2)` and `f((1)/(3))lt (1)/(3)`

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The correct Answer is:
C
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