• geerky42
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 $$\displaystyle \int_0^1 f_a^b(x)~\mathrm dx$$"
Mathematics
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• geerky42
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 $$\displaystyle \int_0^1 f_a^b(x)~\mathrm dx$$"
Mathematics

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