# Down the rabbit hole ......

Calculus Level 5

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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