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When I did further maths at college, we spent a couple of hours on a particular kind of integration, where the function was integrated with respect to the length of the path along the function, typically starting at the point x = 0, y = f(0), and typically calling the path length variable s. I remember that this was curious for all sorts of reasons, but not any specific reason.

It may have been called implicit integration, but googling for that phrase seems to suggest I am remembering it wrong.

I get puzzled looks every time I describe this to people who have studied maths for years for some reason. Does this sound familiar and if so, what's the common name for this?

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    @MichaelHardy I do, yes. I'm starting to doubt that the function was expressed in cartesian coordinates, but I don't see how polar would change anything... Perhaps the graph was described by a function of the length along the graph, rather than y = f(x), does this ring a bell? Sorry, not my best question :)2012-02-14

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I've found it! It was called an intrinsic equation, and presumably we integrated it to obtain a cartesian representation.

Perhaps there was no special term for the integration; maybe it was something like "Integrating an intrinsic curve".

There are obviously a few things I got wrong in the question, which made answering it a bit of a guesswork.

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    Great then. Can you accept your own answer? (If your doubts have been cleared, obviously)2012-02-23