Integration (9)

Calculus Level 4

Let \(f\left( x \right)\) is a continuous function which takes only positive values for

\(x\ge 0\) and satisfy \(f\left( 1 \right) =0.5\)

and \(\int _{ 0 }^{ x }{ f\left( t \right) dt} =x\sqrt { f\left( x \right) } \).

Then the value of \(\frac { 1 }{ f\left( \sqrt { 2 } +1 \right) } \)

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