Results 1 to 7 of 7

Math Help - Length of C

  1. #1
    Member
    Joined
    Sep 2007
    Posts
    94

    Length of C

    I'm not too bad on this section of the book but this question has got me stumped.

    Let C be the curve of intersection of the parabolic cylinder x^2 = 2y and the surface 3z = xy. Find the exact length of C from the origin to the point (6, 18, 36).

    I can't remember where in my notes we tackled a problem like this.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Undefdisfigure View Post
    I'm not too bad on this section of the book but this question has got me stumped.

    Let C be the curve of intersection of the parabolic cylinder x^2 = 2y and the surface 3z = xy. Find the exact length of C from the origin to the point (6, 18, 36).

    I can't remember where in my notes we tackled a problem like this.
    The curve can be defined parametrically as:

    x = t

    y = \frac{t^2}{2}

    z = \frac{xy}{3} = \frac{t^3}{6}

    The point (0, 0, 0) corresponds to t = 0. The point (6, 18, 36) corresponds to t = 6.

    And you know how to get the arc length of a curve defined parametrically using the formula

    L = \int_{t = a}^{t = b} \sqrt{\left( \frac{dx}{dt} \right)^2 + \left( \frac{dy}{dt} \right)^2 + \left( \frac{dz}{dt} \right)^2} \, dt,

    right?


    ps: You might find the following identity useful: t^4 + 4t^2 + 4 = (t^2 + 2)^2 .....
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Sep 2009
    Posts
    82
    Hey could you show me/get me started on how you transformed the two equations to one parametric equation? It would be greatly appreciated

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by snaes View Post
    Hey could you show me/get me started on how you transformed the two equations to one parametric equation? It would be greatly appreciated

    Thanks!
    Since z is defined in etrms of x and y, you only need to think about how to define the curve x^2 = 2y parametrically. There ar an infinite number of choices. I made the simplest one: let x = t. If x = t, what does y have to equal?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Sep 2009
    Posts
    82
    oh ok that how...thanks!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2009
    Posts
    1

    Wrong answer?

    Mr. Fantastic i followed the steps you provided and my end result was 1/3 +2 which i converted to 7/3 however thats still wrong why's that?


    and as to how i got to that answer
    ______________________
    L = integral from 0-1 ( t^2 +2 t)^2
    which when integrated gives you 1/3t^3 + 2t (limit form 0-1)

    ... in the end my answer is 7/3 ... how's that wrong?
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by Peter1765 View Post
    Mr. Fantastic i followed the steps you provided and my end result was 1/3 +2 which i converted to 7/3 however thats still wrong why's that?


    and as to how i got to that answer
    ______________________
    L = integral from 0-1 ( t^2 +2 t)^2
    which when integrated gives you 1/3t^3 + 2t (limit form 0-1)

    ... in the end my answer is 7/3 ... how's that wrong?
    The correct integral (after simplifying) is {\color{red}\frac{1}{2}} \int_0^{\color{red}6} t^2 + 2 \, dt.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Arc Length and Chord Length
    Posted in the Trigonometry Forum
    Replies: 7
    Last Post: December 22nd 2010, 01:24 AM
  2. Length needed from a known length and angle
    Posted in the Geometry Forum
    Replies: 4
    Last Post: July 21st 2009, 06:17 AM
  3. arc length and parameterized curve length
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 5th 2008, 02:33 AM
  4. Arc length and chord length
    Posted in the Geometry Forum
    Replies: 8
    Last Post: December 19th 2007, 03:20 PM
  5. Another arc length
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 25th 2007, 02:14 PM

Search Tags


/mathhelpforum @mathhelpforum