Results 1 to 3 of 3

Math Help - length of a curve

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    75

    length of a curve

    find the length of the curve r(t)=2t^(3/2)i + cos(2t)j + sin(2t)k 0<t<1.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Random Variable's Avatar
    Joined
    May 2009
    Posts
    959
    Thanks
    3
     x = 2t^{3 \over 2}

     y = \cos (2t)

     z = \sin (2t)

    then the length of the curve is

     \int_{0}^{1} \sqrt{ \big(\frac{dx}{dt}\big)^2 + \big(\frac {dy}{dt}\big)^2 + \big(\frac{dz}{dt}\big)^2} \ dt
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    In general

    s= integral (sqrt[(dx/dt)^2 +(dy/dt)^2 + (dz/dt)^2]dt)

    here s = int (sqrt[9t+ 4])

    Let u = 9t + 4

    du = 9dt

    s = 1/9intsqrt(u) = 2/27(9t+4)^(3/2) from 0 to 1

    s = 2/27(13^3/2- 8)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Length of a curve
    Posted in the Calculus Forum
    Replies: 6
    Last Post: December 6th 2010, 12:24 PM
  2. Length of a curve
    Posted in the Calculus Forum
    Replies: 13
    Last Post: March 29th 2009, 05:32 PM
  3. arc length and parameterized curve length
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 5th 2008, 03:33 AM
  4. length of curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 19th 2007, 06:21 PM
  5. length of curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 6th 2007, 09:54 PM

Search Tags


/mathhelpforum @mathhelpforum