Let `f` be a non-negative function defined on the interval `[0,1]`. If `int_0^xsqrt(1-(f\'(t))^2)dt=int_0^xf(t)dt, 0lexle1` and `f(0)=0`, then (A) `f(1/2)lt1/2` and `f(1/3)gt1/3` (B) `f(1/2)gt1/2` and `f(1/3)gt1/3` (C) `f(1/2)lt1/2` and `f(1/3)lt1/3` (D) `f(1/2)gt1/2` and `f(1/3)lt1/3`

Options

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 `

Answer

C