How would you integrate Cantor's function

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Integrating Cantor's function over the interval from 0 to 1 involves recognizing its symmetry, as the function is self-similar and can be treated as an infinite piecewise function. The integral can be approached by noting that 1 minus the function, 1-f(x), mirrors the original function but in reverse, allowing the use of symmetry to simplify calculations. The integral of both f(x) and 1-f(x) over the interval yields the same result, facilitating the integration process. This symmetry can be exploited similarly to integrating sine functions over symmetric intervals. Ultimately, understanding the properties of Cantor's function is crucial for successfully integrating it.
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On the interval from 0 to 1?
Thanks
 
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integrating cantor's function

How would you integrate it from 0 to 1? For those of you who don't know what it is here is a link http://en.wikipedia.org/wiki/Cantor_function.
Is it possible to do this as some sort of geometric series? Any help would be appreaciated.
Thanks
 
It looks like itself upside down.
 
Well how can I integrate it? It's almost like an infinite piece wise function.
 
If its integral (over the range [0,1]) exists, let it be I, StatusX's hint was that 1-f(x) is the same function but going downhill not uphill, so the integral of 1-f(x) over [0,1] is also I. You can do the rest from here surely. The point is the function is very symmetric, so you can exploit that symmetry, just like you can integrate sin(x) from -t to t for any t without knowing the indefinite integral of sin(x).
 

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