BigMoosie Posted February 10, 2006 Share Posted February 10, 2006 I am interested in knowing how to find the distance along a function between two values. I am surprised to see that this kind of problem is never encountered in the highest level mathematics in high schools in Australia and decided to research it myself. I would appreciate a term that might be useful to google or perhaps a link to a wiki article or something. Thankyou, BigMoosie Link to comment Share on other sites More sharing options...
Tom Mattson Posted February 10, 2006 Share Posted February 10, 2006 This problem is treated in every calculus book. You'll find it in the index under "arc length". Link to comment Share on other sites More sharing options...
timo Posted February 10, 2006 Share Posted February 10, 2006 Can you perhaps draw a diagram of what you mean? The length of a curve? That´s usually calculated by integrating over the magnitude of the derivative with respect to a curve-parameter (integration is over the curve-parameter). Physics Example: A particle has a trajectory x(t). The length of its path between x(t=0) and x(t=1) is [math] L = \int_0^1 \| dx/dt \| dt = \int_0^1 \| v\| dt[/math]. not sure if that´s what you meant, though. Link to comment Share on other sites More sharing options...
BigMoosie Posted February 11, 2006 Author Share Posted February 11, 2006 Thankyou both, it seems I was after arc length and this is the formula I was looking for: [math]L = \int_0^1 \sqrt{1 + [f'(x)]^2}[/math] Link to comment Share on other sites More sharing options...
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