Down the rabbit hole ......

Calculus Level 4

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

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

Now let S=32f(x)dxS = \displaystyle\int_{\sqrt{3}}^{2} f(x) dx. Compute 100×S\lfloor 100 \times S \rfloor.

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