$s(t)=\int_{t_0}^{t}\left | R'(\xi) \right |d\xi$ What is $\xi$

$s(t)=\int_{t_0}^{t}\left | R'(\xi) \right | d\xi$
What is $\xi$ ?

In the above arc length formula with ##\xi##, what is ##\xi##?

A variable. R' seems to be a function of $\xi$.

I found this equation while studying vector calculus/ multivariable calculus. I was studying about binormal, tangent, normal, frenet frame, etc.

I just don't understand ##\xi## because the variables usually involved were t and s

$\xi$ is just a mute variable. You can't use t inside the integral because t is used on the boundary of the interval. So $\xi$ is just a normal variable.

I found this equation while studying vector calculus/ multivariable calculus. I was studying about binormal, tangent, normal, frenet frame, etc.

I just don't understand ##\xi## because the variables usually involved were t and s

t and s are just letters. You can denote a variable by whatever symbol you want.

I guess ##\xi## is just t, because the integral is from ##t_0## to ##t## so it just has to be t in the sense that it represents time...
I just found it confusing why he suddenly put ##\xi## when all along he was talking about t, s, velocity, binormal, and Frenet frames of vectors
Thanks now I understand !

Last edited:
cepheid
Staff Emeritus
EDIT: Thread title fixed 