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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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    $\begingroup$ How about "line integral" ? $\endgroup$ Commented Feb 14, 2012 at 14:16
  • $\begingroup$ Also called the Contour Integral. $\endgroup$
    – user21436
    Commented Feb 14, 2012 at 14:18
  • $\begingroup$ @TheChaz In that course, the function to be integrated was not a field; more like f(x) = sin(x). Which brings the question of what exactly was integrated; I believe it was the Y of the point. $\endgroup$ Commented Feb 14, 2012 at 14:22
  • $\begingroup$ How about "finding arc length with integration"? $\endgroup$ Commented Feb 14, 2012 at 14:29
  • $\begingroup$ @TheChaz Not that. On further thought, I don't think it was the Y that got integrated; that doesn't make much sense. Perhaps the tangent angle relative to that at the starting point?... $\endgroup$ Commented Feb 14, 2012 at 15:21

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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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  • $\begingroup$ Great then. Can you accept your own answer? (If your doubts have been cleared, obviously) $\endgroup$
    – Pedro
    Commented Feb 23, 2012 at 21:02

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