MATLAB: Numerical integration __ integral limits being variables

numerical integration

Hello, I want to numerically integrate functions whose upper limits x, lower limits 0. Say;

int_0^x f(x) dx

Which method should I use. trapz, simpson, or omething else and which command ?

I mean can you send a simple example of doing this please? Thanks

Best Answer

There are a number of ways you can proceed. One way is to use 'int' with a variable upper limit. See:

   http://www.mathworks.com/help/symbolic/int.html

If that does not succeed (which often happens) you can do numerical integration using the 'cumtrapz' function which also allows you to have a variable, though discrete, upper limit. See

   http://www.mathworks.com/help/matlab/ref/cumtrapz.html

Finally, there are several functions in the File Exchange which are numerical but have higher precision. I wrote one of these. It is located at:

   http://www.mathworks.com/matlabcentral/fileexchange/19152-cumulative-cubic-integration

Related Solutions

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)])

MATLAB: How to create 1*101 of some integer array

Yo have:

A = zeros(1,101);

and then later you have

cumtrapz(x,-4*A);

all elements of A are zero so -4*A is going to be still zero.

change A=zeros(1,101) to A=ones(1,101)

Also as imageAnalyst said, the third argument for linspace is not the spacing so you need to change the code to something like this

x=linspace(0,1,101);
A=ones(1,101);
cumtrapz(x,-4*A);

By the way, are you sure you want to use cumtrapz()? don't you want the output of trapz()?

Best Answer

Related Solutions

MATLAB: Numerical integration using cumtrapz

MATLAB: How to create 1*101 of some integer array

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