simpsons rule for area under the curve in matlab

To use Simpson's rule for area under the curve in MATLAB, you can define a function that represents the curve you want to integrate, and then use the integral function to perform the integration numerically. Here's an example:

main.m
% Define the function to integrate
f = @(x) sin(x);

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

% Use Simpson's rule with the integral function
A = integral(f,a,b,'Simpson');

% Display the result
fprintf('The area under the curve is approximately %.4f.\n',A);
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In this example, we define the function f(x) = sin(x) and the limits of integration a = 0 and b = pi/2, which correspond to the interval [0,pi/2]. We then use the integral function with the 'Simpson' option to perform the integration, and store the result in the variable A. Finally, we display the approximate area under the curve using fprintf.