Results 1 to 3 of 3

Math Help - Integral of a derivative squared.

  1. #1
    Newbie
    Joined
    Jul 2012
    From
    Canada
    Posts
    2

    Integral of a derivative squared.

    How do I find the integral of a derivative that has been squared? (i.e. ∫(dy/dx)^2 dx) An example would be integrating velocity squared, with respect to time.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,406
    Thanks
    1294

    Re: Integral of a derivative squared.

    It would depend on what your DE is and whether it is solvable using methods like separation of variables, integrating factor, substitution, etc.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jul 2012
    From
    Canada
    Posts
    2

    Re: Integral of a derivative squared.

    Well, specifically, I want to integrate this equation:

    Integral of a derivative squared.-capture.jpg

    (Where θ_2 with two dots is an angular acceleration, θ_2 with one dot is an angular velocity, θ_1 and θ_2 are angles, and g, l_1, and l_2 are constants)

    It is an equation of motion for a double pendulum. I want to be able to integrate it numerically between two time values so that I get the total angle moved by a pendulum arm over that time period. I have only learned a little integration, so I am quite lost as to how to do this. The squared angular velocity is my biggest difficulty, as I'd like to be able to integrate that term to have an angle as a result. Also, I am confused as to how I would deal with the angles in the equation, because they are variables and would have different values at every time. Would I just input the angles at t_1 and the angles at t_2 and do the subtraction? I'm not sure if what I want to do is even possible, but any help is much appreciated!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integral of ln Squared?
    Posted in the Calculus Forum
    Replies: 9
    Last Post: May 1st 2010, 04:12 PM
  2. what is the derivative of r = t squared/8 + 1 ?
    Posted in the Pre-Calculus Forum
    Replies: 5
    Last Post: February 18th 2010, 04:39 PM
  3. Derivative of a Squared Trignometric Function
    Posted in the Calculus Forum
    Replies: 12
    Last Post: November 7th 2009, 11:18 AM
  4. Integrate second derivative squared.
    Posted in the Calculus Forum
    Replies: 19
    Last Post: September 18th 2009, 07:39 AM
  5. Sine squared integral
    Posted in the Calculus Forum
    Replies: 4
    Last Post: November 16th 2007, 09:02 AM

Search Tags


/mathhelpforum @mathhelpforum