AREA BETWEEN TWO GRAPH

CHECK IT

%area
clear all;
syms x;

% Define the two functions
f = x^4 - 4*x^2 + 4;   % First curve: f(x) = x^4 - 4*x^2 + 4
g = x^2;               % Second curve: g(x) = x^2

% 1. Find points of intersection
intersection_points = solve(f == g, x);     % Solve for the intersection points
intersection_points = double(intersection_points);  % Convert symbolic to numeric

% Display intersection points
disp('Intersection points:');
disp(intersection_points);

% 2. Initialize total area
total_area = 0;

% Loop over each interval between consecutive intersection points
for i = 1:length(intersection_points)-1
    % Midpoint of the current interval
    mid_point = (intersection_points(i) + intersection_points(i+1)) / 2;
    
    % Evaluate the functions at the midpoint to determine which is on top
    f_mid = double(subs(f, x, mid_point));
    g_mid = double(subs(g, x, mid_point));
    
    if f_mid > g_mid
        top_function = f;
        bottom_function = g;
    else
        top_function = g;
        bottom_function = f;
    end
    
    % 3. Compute the area for this interval
    area = int(top_function - bottom_function, x, intersection_points(i), intersection_points(i+1));
    area_value = double(area);
    
    % Add this area to the total
    total_area = total_area + area_value;
end

% Display the total area of the common region
fprintf('Total area of the common region: %.5f\n', total_area);

% 4. Plot the curves and the shaded regions
figure;
fplot(f, [intersection_points(1)-1, intersection_points(end)+1], 'b-', 'LineWidth', 2); hold on;
fplot(g, [intersection_points(1)-1, intersection_points(end)+1], 'r-', 'LineWidth', 2);

% Shade the regions between the curves
for i = 1:length(intersection_points)-1
    x_vals = linspace(intersection_points(i), intersection_points(i+1), 1000);
    
    % Recalculate which function is on top for the current interval
    mid_point = (intersection_points(i) + intersection_points(i+1)) / 2;
    f_mid = double(subs(f, x, mid_point));
    g_mid = double(subs(g, x, mid_point));
    
    if f_mid > g_mid
        y_top = double(subs(f, x, x_vals));
        y_bottom = double(subs(g, x, x_vals));
    else
        y_top = double(subs(g, x, x_vals));
        y_bottom = double(subs(f, x, x_vals));
    end
    
    % Fill the region between the curves
    fill([x_vals, fliplr(x_vals)], [y_top, fliplr(y_bottom)], 'g', 'FaceAlpha', 0.3);
end

% legend('f(x) = x^4 - 4x^2 + 4', 'g(x) = x^2', 'Common Region');
% xlabel('x');
% ylabel('y');
% title('Area of the Common Region Between Two Curves');
% grid on;
% hold off;