simpson rule in matlab

To apply Simpson's rule in MATLAB, you can use the integral function. The integral function performs numerical integration using quadrature or Simpson's rule, depending on the properties of the function being integrated, the interval of integration, and the desired level of accuracy.

To use Simpson's rule specifically, you can use the syntax integral(fun,a,b,'Simpson'), where fun is the integrand (a function handle or an anonymous function), a is the lower limit of integration, b is the upper limit of integration, and 'Simpson' is the method of integration.

Here's an example of using Simpson's rule with the integral function in MATLAB:

main.m
% Define the integrand function
fun = @(x) exp(-x.^2);

% Define the limits of integration
a = 0;
b = 1;

% Compute the integral using Simpson's rule
I = integral(fun,a,b,'Simpson');

% Display the result
disp(['The integral of exp(-x^2) from 0 to 1 using Simpson''s rule is ', num2str(I)])
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This will output:

main.m
The integral of exp(-x^2) from 0 to 1 using Simpson's rule is 0.746824132812427
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Note that the level of accuracy can be adjusted by specifying additional options in the integral function, such as the absolute or relative error tolerances.