simpsons rule in matlab

Simpson's rule is a numerical method used for approximating definite integrals. It works by approximating the area under a curve by using a quadratic function that passes through three points. MATLAB provides the built-in function quad for numerical integration. Here's an example of how you could use quad to apply Simpson's rule:

main.m
% Define the integrand function
f = @(x) x.^2 + 2.*x + 1;

% Define the limits of integration
a = 0;
b = 2;

% Apply Simpson's rule using quad
I = quad(f, a, b, 'Simpson');

% Display the result
fprintf('Approximate value of integral using Simpson''s rule: %f\n', I);
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In this code, we define the integrand function f as x.^2 + 2.*x + 1, which is the function we want to integrate. Then we define the limits of integration a and b. To apply Simpson's rule, we call quad with the arguments f, a, b, and 'Simpson'. The output of quad is the approximate value of the integral. We display the result using fprintf.