How to calculate the area under the curve with data given on an excel file, and not using the function "trapz"?

Create a MATLAB program to calculate the area under the curve for the strain-stress. The goal of the project is to have a MATLAB script that automatically reads the experimental data set. The MATLAB script must not use native functions like “trapz” in the calculation of the area. The goal is to calculate the area under the stress-strain curve.

[James Tursa]

Are you supposed to write your own Euler or trapz function for this?

[Andres Gustavo Ambriz Gudiel]

Euler. I can't use any "trapz" function.

[James Tursa]

I meant are you supposed to write your own area calculator function from scratch? (be it Euler or trapezoid or whatever)

[Andres Gustavo Ambriz Gudiel]

Yes, indeed. Everything from scratch. Thank you.

Answer 1

[Scott MacKenzie]

f = 'https://www.mathworks.com/matlabcentral/answers/uploaded_files/702117/Steel6150Tens.csv';
T = readtable(f);
T(end,:) = []; % remove last row, outlier

x = T.Strain;
y = T.Stress;
plot(x,y)

% compute area the hard way
a0 = 0; 
for i=2:length(x)
    a0 = a0 + (x(i)-x(i-1)) * (y(i)+y(i-1))/2;
end
fprintf('Area: %f\n', a0);

Area: 163.079188

% verify result using trapz
a1 = trapz(x, y);
fprintf('Area using trapz: %f\n', a1);

Area using trapz: 163.079188

[James Tursa]

This is obviously homework ...

[Scott MacKenzie]

Hmm, yes, I suppose so. Maybe marks will be deducted for using a loop!

[Andres Gustavo Ambriz Gudiel]

I am studying for my course that I will take next semester. I am just trying to solve this in different ways, if it is possible.

[Andres Gustavo Ambriz Gudiel]

What method did you use for the code on “compute area the hard way”?

[Scott MacKenzie]

OK, good luck with your course. When you post questions pertaining to your course, it's best to try to code-up an answer first. Then, post the code and ask a question about something that isn't working quite the way you expect.

BTW, you can also solve the question here using the polyarea and integral functions. For integral, you need to have an equation for the curve.

[Scott MacKenzie]

Concering your question ("what method..."), the "hard way" approach sums the area of the rectangles formed by the x- and y-coordinates of the curve with respect to the x-axis. This is the way the concept of integration is usually demonstrated in textbooks. Just Google "area under the curve using integration" (or something like that).

[Andres Gustavo Ambriz Gudiel]

Thank you. I appreciate it . I”ll do it next time.

[Wan Ji]

By using 'type trapz' command, one can see the vectorized trapz method, the code is simplified as:

z = diff(x,1,1).' * (y(1:end-1,:) + y(2:end,:))/2;