This is my first post, so hello forums

. Anyway, I am trying to relearn calculus, took a hiatus for a while, and I am currently taking beginners multi-variable calculus and I hit an example that I do not understand in my book (probably cause my diff/integral calculus could use some boning up

).

This involves Arc Length and Curvature:

r(t) = cos(t)i + sin(t)j + tk from point (1,0,0) to (1,0,2$\displaystyle \pi$)

they show that $\displaystyle \mid r\prime (t)\mid = \sqrt{(-sin (t))^2 + cos^2 (t) + 1} = \sqrt{2}$

and then they say "The arc from (1,0,0) to (1,0,2$\displaystyle \pi$) is described by the parameter interval $\displaystyle 0 \leq t \leq 2\pi$ and so [from formula 3], we have...

$\displaystyle L = \int_0^{2\pi} \mid r\prime (t)\mid dt\ = \int_0^{2\pi} \sqrt{2} dt = 2\sqrt{2\pi}$

I do not understand how they got $\displaystyle 2\sqrt{2\pi}$?

shouldn't it be $\displaystyle 2\pi\sqrt{2}$?

Thank you for any and all input