monte carlo integration in matlab

Here is a simple implementation of Monte Carlo integration in MATLAB:

main.m
% Define the function you want to integrate
func = @(x) exp(-x.^2);

% Define the lower and upper limits of integration
lower_limit = 0;
upper_limit = 1;

% Define the number of random points to generate
num_points = 100000;

% Generate random points in the integration range
x = lower_limit + (upper_limit - lower_limit) * rand(num_points, 1);

% Evaluate the function at these points
y = func(x);

% Estimate the integral by taking the mean of the function values multiplied by the integration range
integral_estimate = mean(y) * (upper_limit - lower_limit);
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In this implementation, we define the function we want to integrate using an anonymous function handle func. We also define the lower and upper limits of integration (lower_limit and upper_limit) and the number of random points to generate (num_points).

We then generate num_points random points between lower_limit and upper_limit using the rand function, and evaluate our function at these points. Finally, we estimate the integral by taking the mean of the function values and multiplying by the integration range ((upper_limit - lower_limit)).

Of course, this is a very basic implementation of Monte Carlo integration and there are several ways to improve its accuracy and efficiency.