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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
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