Let $f$ be a non-negative function defined on the interval $[0,1]$. If $\int_0^x \sqrt{1-\left(f^{\prime}(t)\right)^2} d t=\int_0^x f(t) d t, 0 \leq x \leq 1$, and $f(0)=0$, then
Select the correct option:
A
$\mathrm{f}\left(\frac{1}{2}\right)<\frac{1}{2}$ and $\mathrm{f}\left(\frac{1}{3}\right)>\frac{1}{3}$
B
$\mathrm{f}\left(\frac{1}{2}\right)>\frac{1}{2}$ and $\mathrm{f}\left(\frac{1}{3}\right)>\frac{1}{3}$
C
f $\left(\frac{1}{2}\right)<\frac{1}{2}$ and f $\left(\frac{1}{3}\right)<\frac{1}{3}$
D
$\mathrm{f}\left(\frac{1}{2}\right)>\frac{1}{2}$ and $\mathrm{f}\left(\frac{1}{3}\right)<\frac{1}{3}$
Hello 👋 Welcome to Competishun – India’s most trusted platform for JEE & NEET preparation. Need help with JEE / NEET courses, fees, batches, test series or free study material? Chat with us now 👇
