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Let f(x)f(x)f(x) be the unique, non-negative real valued function with domain [1,∞)[1, \infty)[1,∞) defined by the equation
f(x)=∫1xtf(t)dtf(x) = \displaystyle\int_{1}^{x} \dfrac{t}{f(t)} dtf(x)=∫1xf(t)tdt.
Now let S=∫32f(x)dxS = \displaystyle\int_{\sqrt{3}}^{2} f(x) dxS=∫32f(x)dx. Compute ⌊100×S⌋\lfloor 100 \times S \rfloor⌊100×S⌋.
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