how to calculate area of circle using monte carlo integration in matlab

main.m
% Step 1: generate random points inside a square
n = 100000; % number of random points
x = 2*rand(n,1) - 1;  % x-coordinates between -1 and 1 
y = 2*rand(n,1) - 1;  % y-coordinates between -1 and 1

% Step 2: count number of points inside the circle
% Circle equation: x^2 + y^2 = r^2
r = 1; % radius of the circle
num_points_inside_circle = sum(x.^2 + y.^2 <= r^2);

% Step 3: Estimate area of the circle
area_square = 4; % area of the square
area_circle = area_square * num_points_inside_circle / n; % ratio of points inside circle to total number of points

fprintf('Estimated area of circle = %f\n', area_circle);
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