Thread: Arc Length and Curvature

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 )

they show that

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



I do not understand how they got ?
shouldn't it be ?







Thank you for any and all input

Originally Posted by Warrenx

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 )

they show that

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



I do not understand how they got ?
shouldn't it be ?







Thank you for any and all input

Dear Warrenx,

It should be . I think in the book they mean, but accidently made the squareroot sign a little longer making it

Hope this helps you.

Originally Posted by Sudharaka

Dear Warrenx,

It should be . I think in the book they mean, but accidently made the squareroot sign a little longer making it

Hope this helps you.

Thank you very much Mr. Sudharaka, was bugging me so much I stopped reading the section.

That's the reason it is standard (except in this textbook, apparently!) to put numbers or variable before the square root symbol- that is while we typically write "2x", we write " ".