Question

Let $f$ be a non-negative function defined on the interval $\left[ {0,1} ight]$. If $\mathop \smallint 
olimits_0^x \,\,\sqrt {1\,\, - \,\,{{\left( {\,f'\left( t ight)} ight)}^2}} \,\,dt = \mathop \smallint 
olimits_0^x \,\,f\,\,\left( t ight)\,\,dt,\,\,0 \le \,\,x\,\, \le 1$ and $f\,\,\left( 0 ight) = 0$, then

Accepted Answer

$f\,\,\left( {\frac{1}{2}} \right)\,\, < \,\,\frac{1}{2}$ and $f\,\,\left( {\frac{1}{3}} \right)\,\, < \,\,\frac{1}{3}$

Answer

$f\,\,\left( {\frac{1}{2}} \right)\,\, < \,\,\frac{1}{2}$ and $f\,\,\left( {\frac{1}{3}} \right)\,\, > \,\,\frac{1}{3}$

Answer

$f\,\,\left( {\frac{1}{2}} \right)\,\, > \,\,\frac{1}{2}$ and $f\,\,\left( {\frac{1}{3}} \right)\,\, > \,\,\frac{1}{3}$

Answer

$f\,\,\left( {\frac{1}{2}} \right)\,\, > \,\,\frac{1}{2}$ and $f\,\,\left( {\frac{1}{3}} \right)\,\, < \,\,\frac{1}{3}$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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