# Integration using Cumtrapz backwards instead of forwards

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Ramses Young on 19 Nov 2021
Commented: Ramses Young on 20 Nov 2021
Hey all, I am trying to create a program that will take distributed point loads from lift generated by a wing and create moment and shear diagrams using numerical integration through cumtrapz
The way I am doing this is by integrating the points and locations which gets me a shear force, but because cumtrapz integrates numerically forward, it technically creates the right graph but backwards from a conventional beam analysis, which creates cuts. Is it possible to make Cumtrapz work backwards? I have attached images of what I want vs what I get for an example
Desired Shear diagram
Obtained Shear Diagram
The obvious solution is just to subtract the maximum value from the graph but this does not encapsulate the essence of what's going on, and also creates a further problem in the bending moment diagram.
Here's the code
L_dist =[10 9 8 7 6 5 4 3 2 1 0];
locations=[0 1 2 3 4 5 6 7 8 9 10];
shear.z = cumtrapz(locations,(L_dist));
figure('Name','shear - z','NumberTitle','off');
plot(locations, shear.z);

Sean de Wolski on 19 Nov 2021
Easy solution is to just flip everything
L_dist =[10 9 8 7 6 5 4 3 2 1 0];
locations=[0 1 2 3 4 5 6 7 8 9 10];
shear.z = flip(cumtrapz(flip(locations),flip(L_dist)));
figure('Name','shear - z','NumberTitle','off');
plot(locations, shear.z);
Ramses Young on 20 Nov 2021
I cant believe I didn't think of this, but you sir are a legend, I really appreciate it.

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