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% Clear workspace and command window
clc;
clearvars;

% Define symbolic variable
syms x;

% Input function and parameters
f_input = input('Enter the function f(x): ', 's');  % Get input as string
f = str2sym(f_input);  % Convert string input to symbolic expression
fL = input('Enter the interval on which the function is defined: ');
yr = input('Enter the axis of rotation y = c (enter only c value): ');
iL = input('Enter the integration limits: ');

% Ensure f is a valid function
if ~isa(f, 'sym')
    error('The input function must be a valid symbolic expression.');
end

% Calculate the volume of the solid of revolution using the disk method
Volume = pi * int((f - yr)^2, iL(1), iL(2));
disp(['Volume is: ', num2str(double(Volume))]);

% Convert symbolic function to a MATLAB function for plotting
fx = matlabFunction(f);  % Change to matlabFunction

% Define ranges for plotting
xvals = linspace(fL(1), fL(2), 201);
xvalsr = fliplr(xvals);
xivals = linspace(iL(1), iL(2), 201);
xivalsr = fliplr(xivals);
xlim = [fL(1), fL(2) + 0.5];
ylim = [min(fx(xvals)), max(fx(xvals))];

% Plot the function and region
figure('Position', [100, 200, 560, 420]);

% Subplot 1: Function plot and filled region
subplot(2, 1, 1);
hold on;
plot(xvals, fx(xvals), 'b-', 'LineWidth', 2);
fill([xvals, xvalsr], [fx(xvals), ones(size(xvalsr)) * yr], [0.8, 0.8, 0.8], 'FaceAlpha', 0.8);
plot([fL(1), fL(2)], [yr, yr], 'r-', 'LineWidth', 2);
legend('Function Plot', 'Filled Region', 'Axis of Rotation', 'Location', 'Best');
title('Function y = f(x) and Region');
xlabel('x-axis');
ylabel('y-axis');
set(gca, 'XLim', xlim);

% Subplot 2: Rotated region
subplot(2, 1, 2);
hold on;
plot(xivals, fx(xivals), 'b-', 'LineWidth', 2);
fill([xivals, xivalsr], [fx(xivals), ones(size(xivalsr)) * yr], [0.8, 0.8, 0.8], 'FaceAlpha', 0.8);
fill([xivals, xivalsr], [ones(size(xivals)) * yr, -fx(xivalsr) + 2 * yr], [1, 0.8, 0.8], 'FaceAlpha', 0.8);
plot(xivals, -fx(xivals) + 2 * yr, 'm-', 'LineWidth', 2);
plot([iL(1), iL(2)], [yr, yr], 'r-', 'LineWidth', 2);
title('Rotated Region in xy-Plane');
xlabel('x-axis');
ylabel('y-axis');
set(gca, 'XLim', xlim);

% Generate and visualize the solid of revolution
[X, Y, Z] = cylinder(fx(xivals) - yr, 100);
Z = iL(1) + Z .* (iL(2) - iL(1));
figure('Position', [700, 200, 560, 420]);
surf(Z, Y + yr, X, 'EdgeColor', 'none', 'FaceColor', 'flat', 'FaceAlpha', 0.6);
hold on;
plot([iL(1), iL(2)], [yr, yr], 'r-', 'LineWidth', 2);
xlabel('X-axis');
ylabel('Y-axis');
zlabel('Z-axis');
view(22, 11);