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

Let f be a non-negative function defined in `[0, pi//2], f'` exists and be continuous for all x and `int_(0)^(x) sqrt(1- (f'(t))^(2)) dt = int_(0)^(x) f(t) dt and f(0)= 0`. Then

A

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

B

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

C

`f((4)/(3)) lt (4)/(3) and f((2)/(3)) lt (2)/(3)`

D

`f((4)/(3)) gt (4)/(3) and f((2)/(3)) gt (2)/(3)`

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