How to Integrate these data ?

Hi All

I have a Diagram of Data x-y like this :

and the integration should look like :

having the Data of the first diagram as :

x=[0: 0.06] , you choose the step

and y = [-0.062847398, -0.057017095, -0.048434094, -0.03892462, -0.030365732, -0.023723144, -0.019435892, -0.017256826, -0.01674607, -0.01734093, -0.018578755, -0.020101786, -0.021674287, -0.023155192, -0.024468152, -0.025585016, -0.026502747, -0.027236393, -0.027807428, -0.02824128, -0.028562468, -0.028794073, -0.028956106, -0.029065736, -0.029136971, -0.029181112, -0.0292069, -0.029220911, -0.029227789, -0.029230507, -0.029230507, -0.029227789, -0.029220911, -0.0292069, -0.029181112, -0.029136971, -0.029065736, -0.028956106, -0.028794073, -0.028562468, -0.02824128, -0.027807429, -0.027236391, -0.026502745, -0.025585016, -0.024468152, -0.023155192, -0.021674288, -0.020101786, -0.018578757, -0.01734093, -0.01674607, -0.017256826, -0.019435894, -0.023723146, -0.030365737, -0.038924627, -0.048434086, -0.057017088, -0.062847398]

How can I integrate on these data so I will have more or less the same final amount of the integration that you see on the second graph : -2e-3 ? I know that my data are not precisely similar as the first graph , but I just would like to know how to do the integration with these data ? thank you

Answer 1

[pfb]

You could use "cumptrapz". For that you'll need to provide both x and y.

In this respect, what do you mean "you choose the step"? If there is "a step" it will be something like the integration integral over the number of sampled points...

[farzad]

Thank you , but how do we use quad when we have the vectors , ok I meant the steps be arbitrary , cause I coudn't choose the write amount so the x and y have the same size , but the quad needs a function though !

[farzad]

Thank you , but shall you please tell me how could I do that

[pfb]

strike that. What you need is "cumtrapz".

I always get mixed up with those, sorry.

I'm correcting my reply.

[Torsten]

Use trapz.

Best wishes

Torsten.

[pfb]

Thorsten, I think he wants the upper bound of integration to run in the whole interval (check the second plot). For that he should use cumtrapz. Trapz would give him a single scalar.

[farzad]

Should I only write :

cumtrapz(y)

??????????

[pfb]

You could read the documentation for cumtrapz, to begin with. Do you want to learn how to do things, or are you just having other people solve your homeworks?????????

The documentation pops up when you type "help cumtrapz" or "doc cumtrapz".

In general the function needs to know the abscissae as well, as I mention above. The result depends on that too. Therefore it should be

 I = cumtrapz(x,y);

I think you know the abscissae, otherwise how could you plot the figure in the first place?

If you just need the integral on the whole interval (as opposed to the second plot) you could use trapz, as suggested by Torsten.

 I = trapz(x,y);

If you do not want to bother with x, and you know the (fixed) step between subsequent points, you can use

 I = dx*trapz(y)