Results 1 to 5 of 5

Math Help - Length of curve

  1. #1
    Member
    Joined
    Jul 2005
    Posts
    187

    Length of curve

    y=3x^3-9x^2
    Domain: [0,3]

    What's the lenght of curve ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,746
    Thanks
    648
    Hello, totalnewbie!

    I can set it up, but I don't see a way to integrate it . . .
    . . Is there a typo?


    y \:=\:3x^3-9x^2
    Domain: [0,3]
    What's the length of curve?

    Formula: . L \;= \;\int^b_a\sqrt{1 + \left(\frac{dy}{dx}\right)^2}\,dx

    We have: . \frac{dy}{dx} \:=\:9x^2 - 18x

    Hence: . L \;=\;\int^3_0\sqrt{1 + (9x^2 - 18x)^2}\:dx \;= \;\int\sqrt{81x^4 - 324x^3 + 324x^2 + 1}\:dx

    . . Good luck!

    Follow Math Help Forum on Facebook and Google+

  3. #3
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    When you have,
    \int \sqrt{P(x)}dx
    Where P(x) is a cubic or quartic polynomial. Usually the integral leads to an "elliptic integral" and fails to be integrated.
    ----
    Using Soroban's integral.
    And Simpson's Rule with 100 terms
    I got,
    \approx 24.3662
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,962
    Thanks
    349
    Awards
    1
    Quote Originally Posted by Soroban View Post
    Hello, totalnewbie!

    I can set it up, but I don't see a way to integrate it . . .
    . . Is there a typo?



    Formula: . L \;= \;\int^b_a\sqrt{1 + \left(\frac{dy}{dx}\right)^2}\,dx

    We have: . \frac{dy}{dx} \:=\:9x^2 - 18x

    Hence: . L \;=\;\int^3_0\sqrt{1 + (9x^2 - 18x)^2}\:dx \;= \;\int\sqrt{81x^4 - 324x^3 + 324x^2 + 1}\:dx

    . . Good luck!

    One can, of course, do it numerically either via the trapezoid or Simpson's rule, to name two of the easier methods. I did it on my calculator and got:
    about 24.3662.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member
    Joined
    Apr 2006
    Posts
    401
    Left sum: 23.5965
    Right sum: 25.1576
    Mid sum: 24.3609
    Trap. rule: 24.377
    Simpson rule: 24.3664

    Compared to 50 intervals.
    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, 11:24 AM
  2. Length of a curve
    Posted in the Calculus Forum
    Replies: 13
    Last Post: March 29th 2009, 04:32 PM
  3. arc length and parameterized curve length
    Posted in the Calculus Forum
    Replies: 1
    Last Post: December 5th 2008, 02:33 AM
  4. length of curve
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 19th 2007, 05:21 PM
  5. length of curve
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 6th 2007, 08:54 PM

Search Tags


/mathhelpforum @mathhelpforum