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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)gt1/3`

C

`f(1/2)lt1/2` and `f(1/3)lt1/3`

D

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

Text Solution

Verified by Experts

The correct Answer is:
C
`f'=+-sqrt(1-f^(2))`
or `f(x)=sinx `or `f'(x)=-sinx` (not possible)
`:. f(x)=sinx`
Also `xgtsinxAAxgt0`
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