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}} d t=\int_{0}^{x} f(t) d t and f(0)=0. Then

Correct Answer is : f(43)<43 and f(23)<23

f(\frac{1}{2}) > \frac{1}{2} and f(\frac{1}{3})

f(\frac{4}{3}) > \frac{4}{3} and f(\frac{2}{3}) > \frac{2}{3}

WBJEE 2022 Math Solved Paper

Question : 52 of 75

Marks: +1, -0

Let f be a non-negative function defined in [0,π∕2],f′ exists and be continuous for all x and

∫

√1−(f′(t))2dt=

∫

f(t)dt and f(0)=0. Then

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