Quick Linear Integration Question

[sriracha]

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.

 

[sriracha]

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.

 

[sriracha]

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).

 

[sriracha]

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_{0},y_{0}, z_{0}). 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 \frac{1}{\Delta h}\int^{\Delta h}_{0} F_{y} - F_{x} dh ?

 

[sriracha]

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.

 

[sriracha]

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.

 

[sriracha]

Also realized this is a "textbook type" problem so you can move it if you want.

 

[bwood01]

http://www.infoocean.info/avatar1.jpg I guess this can't be right because F_x can depend on y and vice-versa.

 

[sriracha]

http://www.infoocean.info/avatar1.jpg I guess this can't be right because F_x can depend on y and vice-versa.

That's what I said.