Let \(f(x)\) be the unique, non-negative real valued function with domain \([1, \infty)\) defined by the equation

\(f(x) = \displaystyle\int_{1}^{x} \dfrac{t}{f(t)} dt\).

Now let \(S = \displaystyle\int_{\sqrt{3}}^{2} f(x) dx\). Compute \(\lfloor 100*S \rfloor\).

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