arc length of a vector

[Erin0702]

Problem: Find the arc length of the curve r(t)=<cos t,sin t,t> when t is greater than or equal to 0 and less than or equal to pi

r(t) is a vector.
I'm not even sure what type of formula to use or really where to go with it...any help would be greatly appreciated!

 

[pka]

Problem: Find the arc length of the curve r(t)=<cos t,sin t,t> when t is greater than or equal to 0 and less than or equal to pi.

Do you remember arc length from Calculus II?
This is about the same idea.

\(\displaystyle \L L = \int\limits_a^b {\left| {r'(t)} \right|dt} = \int\limits_a^b {\sqrt {x'(t) + y'(t) + z'(t)} dt}\)

 

[Erin0702]

Thanks! I remembered that formula but I wasn't sure what to do about the Z point so thanks for the help!

 

[Erin0702]

So I would have the integral from 2 pi to 0...and then the sqrt of (sin(t)-cos(t)+1)dt. but where do I go from here to integrate it? u substitution?