determine the centroidal element ybar by finding the midpoint of the lower and upper curves. in matlab

main.m
% Define the lower and upper curves of the shape
lower_curve = @(x) x.^2;
upper_curve = @(x) x.^3;

% Define the range of x values to plot
x = linspace(0, 1);

% Plot the shape
hold on;
plot(x, lower_curve(x));
plot(x, upper_curve(x));
xlabel('x');
ylabel('y');

% Find the midpoint of each line segment
for i = 1:length(x)-1
    x1 = x(i);
    x2 = x(i+1);
    y1 = lower_curve(x1);
    y2 = lower_curve(x2);
    midpoint1 = [(x1 + x2)/2, (y1 + y2)/2];
    
    y1 = upper_curve(x1);
    y2 = upper_curve(x2);
    midpoint2 = [(x1 + x2)/2, (y1 + y2)/2];
    
    midpoints(i,:) = (midpoint1 + midpoint2)/2;
end

% Compute the centroidal element
ybar = mean(midpoints(:,2));

% Plot the centroidal element
plot([0,1], [ybar,ybar], 'k--');
legend('Lower curve', 'Upper curve', 'Centroidal element');
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