MATLAB: How to integrate a data set

data setintegrate

I have a data set that includes data for temperature and specific heat capacity, and I need to integrate (Cv(T)/T)dT and (Cv(T))dT over 0 to 270. I uploaded the data into Matlab already, and I have a plot of the data (temp on x-axis, Cv on y-axis). How do I code for the cumulative entropy (see first equation) and energy (see second equation)?

Best Answer

I would use the trapz function, or cumtrapz (linked to in the trapz documentation), depending on the result you want.

For example:

IntEq1 = trapz(T, Cv./T);
IntEq2 = trapz(T,Cv);

Without your data I am only guessing here, however these should at least be close to what you want. If you want vectors of interim results as well, replace trapz with cumtrapz in these assignments.

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MATLAB: How can i calculate area under curve from CSV file.

It would help to see the .csv file.

Apparently, ‘t’ was converted to a duration array in the process of reading it.

Try this:

t = minutes(1:200);                                                 % Duration Array
ActivePowerANAvg = [zeros(1,50) ones(1,100)*6500 zeros(1,50)];      % Create Vector
tv = datenum(t);                                                    % Convert To Numeric VEctor
Integral = cumtrapz(tv,ActivePowerANAvg);                           % Integrate (Using ‘cumtrapz’ For The Plot)
figure
yyaxis left
plot(t, ActivePowerANAvg)                                           % Plot Signal As Duration
yyaxis right
plot(t, Integral)                                                   % Plot Integral As Duration

I use cumtrapz for the plot, use trapz to get only the end result. The code is otherwise the same.

EDIT — (13 Mar 2021 at 15:00)

Added plot figure —

MATLAB: Numerical integration using cumtrapz

The cumtrapz function integrates a vector, and ideally, the dependent variable vector with respect to the independent variable vector.

The limits of the independent variable vector are the limits of the integration, so for example:

x = 0:42;
y = randn(size(x));
Int_y_dx = cumtrapz(x, y);
figure
yyaxis left
plot(x, y)
ylabel('$y(x)$', 'Interpreter','latex')
yyaxis right
plot(x, Int_y_dx)
ylabel(sprintf('$\\int_{%d}^{%d}y(x)\\ dx$',min(x),max(x)), 'Interpreter','latex', 'FontSize',14)
grid
xlim([min(x) max(x)])

Best Answer

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MATLAB: How can i calculate area under curve from CSV file.

MATLAB: Numerical integration using cumtrapz

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