Function integral

Calculus Level 3

A continuous real function \(f\) satisfies \(f(2x)=3f(x)\) for all real \(x\). If \(\displaystyle\int _{ 0 }^{ 1 }{ f\left( x \right) \, dx=1 }\), then compute the value of definite integral\( \displaystyle \int _{ 1 }^{ 2 }{ f\left( x \right) \, dx } \).

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