Integral of an Unknown Function

Calculus Level 3

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

01f(x)dx=100,\int_0^1 f(x) dx = 100,

then what is the value of

02f(x)dx?\int_0^2 f(x)dx ?

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