Functional for the distance between two point.

[resurgance2001]

I am told in various places that the functional for the distance between two points is given as the second equation in the attached photo.

My question is how is that functional derived please. I know it is something I should already know from calculus but it is confusing me not being able to remember where the equation comes from. Thanks

 

[resurgance2001]

I am not quite sure why the system uploaded three copies (edited to one now) of my photo. God I feel old. My first attempt - I am also looking for instructions on how to use latex or whatever on this website that is used for writing equations.

 

[Dr.Peterson]

Here is a good place to review calculus:

Calculus II - Arc Length

In this section we’ll determine the length of a curve over a given interval.

tutorial.math.lamar.edu

To use LaTeX on this site, see

LaTeX Math Formatting is Available

A system named LaTeX is available in the forum, to generate math symbols and formatting. Using LaTeX requires learning programming codes and syntax. Tutorials and examples are available on the Internet, and some references and links appear below. (As an alternative to LaTeX, the purplemath site...

www.freemathhelp.com

 

[pka]

I am also looking for instructions on how to use latex or whatever on this website that is used for writing equations.

Each of these: x^2, x^2-3x+9, \sqrt{x^2=4}, \dfrac{x}{x^2-1}, \min\{34, 62\} will give in surrounded \(\(\)\)
\(x^2,\quad x^2-3x+9,\quad \sqrt{x^2=4},\quad \dfrac{x}{x^2-1},\quad \min\{34, 62\}\)

 

[HallsofIvy]

Interesting. I find that both [ t e x ] ,[/ t e x ] and [m a t h], [/ m a t h] (without the spaces) work: \(\displaystyle x^2\), [math]x^3[/math]. Some boards allow you to use "$" at beginning and end but that does not work here: $x^2$.