Let \( f(x) \) is a continuous function which takes positive values...

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Let \( f(x) \) is a continuous function which takes positive values for \( x \geq 0 \) and satisfy \( \int_{0}^{x} f(t) d t=x \sqrt{f(x)} \)
\( \mathrm{P} \)
W with \( f(1)=\frac{1}{2} \). Find the value of \( f(\sqrt{2}+1) \).
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