# Quick Linear Integration Question

1. Mar 20, 2012

### 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.

2. Mar 20, 2012

### 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.

3. Mar 20, 2012

### 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).

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4. Mar 20, 2012

### 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 ?

5. Mar 20, 2012

### 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.

6. Mar 20, 2012

### 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.

7. Mar 20, 2012

### sriracha

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

8. Mar 20, 2012

### bwood01

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
9. Mar 20, 2012

### sriracha

That's what I said.

Last edited by a moderator: May 5, 2017