Results 1 to 5 of 5

Thread: Arc lengh of some curves

  1. #1
    Junior Member
    Joined
    Nov 2015
    From
    Romania
    Posts
    40

    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)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,572
    Thanks
    1710

    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
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2015
    From
    Romania
    Posts
    40

    Re: Arc lengh of some curves

    I did the first one, any ideea for the second one?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Nov 2015
    From
    Romania
    Posts
    40

    Re: Arc lengh of some curves

    I tried the substitution t=sin(u) didnt work...
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    6,572
    Thanks
    1710

    Re: Arc lengh of some curves

    Can you show us your working out?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Curves
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: Nov 14th 2011, 10:55 AM
  2. [SOLVED] Curves in R^3
    Posted in the Differential Geometry Forum
    Replies: 0
    Last Post: Feb 9th 2011, 10:44 AM
  3. curves
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Dec 15th 2008, 04:29 PM
  4. curves
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Apr 12th 2008, 04:27 PM
  5. sketching curves-transformation curves f(x)!!!!
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: Dec 2nd 2006, 06:55 AM

/mathhelpforum @mathhelpforum