Distance along curves

[BigMoosie]

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

[Tom Mattson]

This problem is treated in every calculus book. You'll find it in the index under "arc length".

[timo]

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.

[BigMoosie]

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]