# Thread: Arc lengh of some curves

1. ## Arc lengh of some curves

1) r(t)=(a*cos(t)*(cos(2t))^(1/2) , a*sin(t)*(cos(2t))^(1/2) , a*t) ; a - real number
So arc lengh is Integral for t1 to t2 of ||r'(t)|| dt , t1<t2
r'(t)=(-a*sin(3t)/(cos(2t))^(1/2) , a*cos(3t)/(cos(2t))^(1/2) , a)

Integral for t1 to t2 of a*(1/cos(2t) + 1)^(1/2) --- can this integral be solved? and if not are there any other methods to find the arc lengh? if yes please show me

2) r(t)=(2a*arcsin(t)+t*(1-t^2)^(1/2) , 2a*t^2 , 4a*t); a - real number
r'(t)=(2a/(1-t^2)^(1/2) + (1-t^2)^(1/2) - t^2/(1-t^2)^(1/2) , 4a*t, 4a)
I tried to find ||r'(t)|| but is not something i can do here? are there any methods? (And please show an example)

2. ## Re: Arc lengh of some curves

Hey Valer.

You should show your attempts at doing this.

Also - for arc-length there is a well known formula you can use.

https://en.wikipedia.org/wiki/Arc_length

3. ## Re: Arc lengh of some curves

I did the first one, any ideea for the second one?

4. ## Re: Arc lengh of some curves

I tried the substitution t=sin(u) didnt work...

5. ## Re: Arc lengh of some curves

Can you show us your working out?