Repost from Brilliant: Can anyone solve this?
"Define \(f_a^b(x)\) as a function which converts \(x\) into base \(a\) and then interprets it as a number in base \(b\).
For example, \(f_2^{10}(0.5)\) will mean first changing \(0.5\) to base \(2\) i.e. \(0.1\) and then interpreting \(0.1\) as a base \(10\) number. That's it!
So, find a general formula for \(\displaystyle \int_0^1 f_a^b(x)~\mathrm dx\)"

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Well, is \(f_a^b(x)\) even continuous function?

that doesn't matter for definite integral right

It doesn't? I'm not sure haha. I'm interesting in solution.

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