Integral of an Unknown Function

Calculus Level 3

Let \(f(x)\) be a real-valued function continuous on \(\left[0,2\right]\) such that \(f(x)=f(2x)\) for all \(x\). If

\[\int_0^1 f(x) dx = 100,\]

then what is the value of

\[\int_0^2 f(x)dx ?\]

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