# Integration without an expression

I'm trying to find the quantity of energy transferred between two systems. I have an absorption curve and a drive curve, but neither of these follow a mathematical expression, they're random squiggely lines.

I want to use the absorption curves to find out how much of the drive is being transferred. I know one way to do this would be to integrate the curves, but they can't really be approximated by an expression.

How else might I go about it?

I have actually thought about drawing them, then doing the old cutting out and measuring the area trick for a rough estimation. Surely there's something easier and more accurate than that though.

Maybe scan them and use something on the computer to find the enclosed area?

But there's a lot of sharp deviation on the curves, so I'd really need to cut the x-axis up into a lot of sections to get any kind of accuracy whatsoever.

Is there any online software that I can draw the curves in (dragging points), or something like that?

Depending on how it crosses the horizontal axis, you may be able to use a planimeter. Otherwise, scan or trace it into a computer and using http://livedocs.adobe.com/en_US/Photoshop/10.0/help.html?content=WS3D3EF585-502B-49d2-85FF-537E9DC25C21.html [Broken] or http://www.ma.iup.edu/projects/CalcDEMma/Green/Green.html [Broken], you can calculate the area contained above the axis/below the axis and take the difference for the proper integral.
Otherwise, do it the old fashioned way: use graph paper to trace and approximate coordinates and use a numerical integration algorithm to calculate the area.

Last edited by a moderator:
Thanks slider, although the problem is more complex than just area. I need to reference this curve to another, and then use the second to find the percentage of the first that's being absorbed, and I need to do this along the entire length of the curves, for at least tens of points, preferably more.

Last edited:
it might be easier to scan it, and then instead of integrating, just count the amount of non-white pixels over the x-axis. then to find the length of the curve, again, just take the number of columns of pixels.
percentages, can just be calculated.

Well, the whole of the line may not have a similar looking function,

But! If you break the line into tiny sub-sections and find the functions

that may match each individual little line, you can simply add all the

integrals of the tiny lines together.

Maybe this will help :)