# 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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