HMMT 2002 K10

A continuous real function $f$ satisfies the identity $f(2 x)=3 f(x)$ for all $x$ . If $\int_{0}^{1} f(x) d x=1$ , what is $\int_{1}^{2} f(x) d x$ ?

Dataset text NuminaMath olympiads. Quoted with source.

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