How to find the area between the x axis and positive section of a graph?

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dada55 on 15 Nov 2015
Commented: Star Strider on 15 Nov 2015
I'm trying to find the 2 separate areas for a Force * Displacement graph. The graph is basically 2 non-perfect, not-symmetrical half ellipses that connect at the x axis.
I need to specifically find the work done (area) for positive and negative forces but not sure how I could do it?
I have the data stored in 2 vectors but is there any way to only find the area of the graph above or below the x axis?
Or is my only choice to truncate the vectors to separate the graph into 2 and use 'trapz' function?
I am a beginner at MATLAB so please go easy on me!
Thank you for any help/tips :)
The reason I dislike the idea of removing the data to separate into positive and negative values of Y axis is because the data alternates and so becomes tiring having to remember which data values to remove from both vectors to maintain the correct plots.
I have found an easy way to separate the Y values from positive to negative (testing(testing < 0) = [];) but then I do not know which elements to delete in the X axis vector (as they can be both +ve and -ve).
If I do trapz(Y_Vector) when it has been separated into positive values, would it work to just multiply by the range of the X_Vector?
dada55 on 15 Nov 2015
I have a vector of Force ( contains both +ve and -ve values) and in plots is the y axis.
and I have a vector of Displacement ( contains both +ve and -ve values, corresponding to both +ve and -ve values of Force) and is the x axis.
edit: Maybe this image of the plots and data can help understand what I have:

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Accepted Answer

Star Strider
Star Strider on 15 Nov 2015
Edited: Star Strider on 15 Nov 2015
Without your data it’s not possible to say definitively. It might be best to separate the positive and negative forces. I would use the trapz or cumtrapz functions, depending on the result you want.
EDIT — I get the impression that the +ve and -ve values of force are each sampled at different values of displacement. If that is correct, you would likely need to integrate the +ve and -ve forces separately. If the force values are sampled at the same values of displacement, you can take the differences and integrate them using trapz. Use the relevant displacement values as your x-vector in each instance.

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More Answers (1)

Image Analyst
Image Analyst on 15 Nov 2015
Why don't you just sum the values above and below the axes
sumAbove = sum(Displacement1(Displacement1 >= 0));
sumBelow = -sum(Displacement1(Displacement1 < 0));
You can multiply by the deltaX spacing if you want calibrated units.

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