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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^x sqrt[1-(f'(t))^2].dt`=`int_0^x f(t).dt`, `0<=x<=1` and 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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