How would you integrate Cantor's function

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    Function Integrate
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Homework Help Overview

The discussion revolves around integrating Cantor's function over the interval from 0 to 1, a topic situated within real analysis and the study of functions. Participants are exploring the properties and behavior of this unique function in the context of integration.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning how to approach the integration of Cantor's function, with some suggesting the possibility of using geometric series. Others note its piecewise nature and symmetry, raising questions about how these characteristics might influence the integration process.

Discussion Status

The discussion is ongoing, with various insights being shared. Some participants have offered hints regarding the symmetry of the function and its implications for integration, while others are still seeking clarity on the integration process itself.

Contextual Notes

There is a mention of the function's symmetry and its piecewise characteristics, which may influence the integration approach. Participants are also referencing external resources for further understanding.

sebastianzx6r
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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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