# 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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