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Let 'f' be a non-negative function defin...

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 le x le 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) 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`

Text Solution

Verified by Experts

The correct Answer is:
C
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