Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Quick Linear Integration Question

  1. Mar 20, 2012 #1
    If my integrand is:

    [F_y (dy/dh) + F_x (dx/dh)] dh

    Can I break this into two integrals, F_y over the y component of dh and F_x over the x component:

    [F_y] (dh)_y + [F_x] (dh)_x

    This is for linear integration over the hypotenuse of a right triangle with equal, undefined Δx Δy sides. F is also undefined.
     
  2. jcsd
  3. Mar 20, 2012 #2
    I guess this can't be right because F_x can depend on y and vice-versa. I will post the question and the work I have done. Please note this is not a homework assignment. I have looked at other similar problems, but none where F is undefined and this is what is giving me problems.
     
  4. Mar 20, 2012 #3
    The problem is attached and I have uploaded my work here: http://i39.tinypic.com/kbd4s4.jpg

    (I wanted to put it in high resolution and the file was too big for PF).
     

    Attached Files:

  5. Mar 20, 2012 #4
    By the way I arbitrarily chose the midpoint of the hypotenuse as my (x,y,z) although I realize now it would make things a bit clearer if I had chosen (x[itex]_{0}[/itex],y[itex]_{0}[/itex], z[itex]_{0}[/itex]). I'm pretty certain this should have no bearing on the work I did on the left.

    I am wondering If I can go ahead and integrate once I have the problem solved to the point where I have [itex]\frac{1}{\Delta h}[/itex][itex]\int[/itex][itex]^{\Delta h}_{0}[/itex] F[itex]_{y}[/itex] - F[itex]_{x}[/itex] dh ?
     
  6. Mar 20, 2012 #5
    That doesn't seem right either because then I'm left with F_y - F_x and I to integrate over h I think I would need to parametrize F_y and F_x. Even if I do, I am left with F_x and F_y of (deltay - h / deltah). I need a respective F_y (x,y,z) *deltay - F_x (x,y,z) * delta x and guess I have no idea how to get there.
     
  7. Mar 20, 2012 #6
    Yay me! Where I found x = deltay - h/deltah and y = h/deltah I realized I could replace the x and ys with F_x and y with F_y then integrate over dh.
     
  8. Mar 20, 2012 #7
    Also realized this is a "textbook type" problem so you can move it if you want.
     
  9. Mar 20, 2012 #8
    http://www.infoocean.info/avatar1.jpg [Broken]I guess this can't be right because F_x can depend on y and vice-versa.
     
    Last edited by a moderator: May 5, 2017
  10. Mar 20, 2012 #9
    That's what I said.
     
    Last edited by a moderator: May 5, 2017
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Quick Linear Integration Question
Loading...