Integration without an expression

[johnintheuk]

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?

 

[slider142]

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 or http://www.ma.iup.edu/projects/CalcDEMma/Green/Green.html , 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.

 

[johnintheuk]

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.

 

[soandos]

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.

 

[AtaraxiaAle]

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 :)