Results 1 to 2 of 2

Math Help - Curvilinear integral doubt

  1. #1
    Member
    Joined
    May 2010
    Posts
    241

    Curvilinear integral doubt

    Hi. I have a doubt with this exercise. I'm not sure about what it asks me to do, when it asks me for the curvilinear integral. The exercise says:

    Calculate the next curvilinear integral:

    \displaystyle\int_{C}^{}(x^2-2xy)dx+(y^2-2xy)dy, C the arc of parabola y=x^2 which connect the point (-2,4) y (1,1)
    I've made a parametrization for C, thats easy: \begin{Bmatrix} x=t \\y=t^2\end{matrix} \begin{Bmatrix} x'(t)=1 \\y'(t)=2t\end{matrix}

    And then I've made this integral:
    \displaystyle\int_{-2}^{1}t^2-2t^3+(t^4-2t^3)2t dt
    But now I'm not too sure about this. What I did was:

    \displaystyle\int_{a}^{b}F(\sigma(t))\sigma'(t)dt

    But now I don't know if I should use the module, I did this: \displaystyle\int_{a}^{b}F(\sigma(t))\sigma'(t)dt and I dont know when I should use this: \displaystyle\int_{a}^{b}F(\sigma(t)) \cdot ||\sigma'(t)||dt

    I mean, both are curvilinear integrals, right?

    I think that I understand what both cases means, but I don't know which one I should use when it asks me for the "curvilinear integral". The first case represents the area between the curve and the trajectory, and the second case represents the projection of a vector field over the trajectoriy, i.e. the work in a physical sense, but I know it have other interpretations and uses.

    Well, thats all. Bye there, thanks for posting.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,513
    Thanks
    1404
    Quote Originally Posted by Ulysses View Post
    Hi. I have a doubt with this exercise. I'm not sure about what it asks me to do, when it asks me for the curvilinear integral. The exercise says:

    Calculate the next curvilinear integral:

    \displaystyle\int_{C}^{}(x^2-2xy)dx+(y^2-2xy)dy, C the arc of parabola y=x^2 which connect the point (-2,4) y (1,1)
    I've made a parametrization for C, thats easy: \begin{Bmatrix} x=t \\y=t^2\end{matrix} \begin{Bmatrix} x'(t)=1 \\y'(t)=2t\end{matrix}

    And then I've made this integral:
    \displaystyle\int_{-2}^{1}t^2-2t^3+(t^4-2t^3)2t dt
    But now I'm not too sure about this. What I did was:

    \displaystyle\int_{a}^{b}F(\sigma(t))\sigma'(t)dt

    But now I don't know if I should use the module, I did this: \displaystyle\int_{a}^{b}F(\sigma(t))\sigma'(t)dt and I dont know when I should use this: \displaystyle\int_{a}^{b}F(\sigma(t)) \cdot ||\sigma'(t)||dt

    I mean, both are curvilinear integrals, right?

    I think that I understand what both cases means, but I don't know which one I should use when it asks me for the "curvilinear integral". The first case represents the area between the curve and the trajectory, and the second case represents the projection of a vector field over the trajectoriy, i.e. the work in a physical sense, but I know it have other interpretations and uses.

    Well, thats all. Bye there, thanks for posting.
    You're correct up to

    \displaystyle \int_{-2}^1{t^2 - 2t^3+(t^4 - 2t^3)2t\,dt}

    \displaystyle = \int_{-2}^1{t^2 - 2t^3 + 2t^5 - 4t^4\,dt}.

    Go from here.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Triple integral, doubt
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 13th 2010, 04:19 AM
  2. Integral doubt
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 9th 2010, 07:28 AM
  3. Replies: 4
    Last Post: October 24th 2009, 02:08 PM
  4. Replies: 4
    Last Post: July 17th 2009, 05:30 AM
  5. Integral curvilinear
    Posted in the Calculus Forum
    Replies: 10
    Last Post: April 26th 2009, 12:07 PM

Search Tags


/mathhelpforum @mathhelpforum