Symbolic Function Calculator and Plotter Menu in MATLAB

 Write a Matlab program that will display a menu, which will let the user to:

1. Enter a function in symbolic format    
2. Displays the nth derivative of the function, n is entered/selected by the user - n can ONLY be 1, 2, or 3.   
3. Calculates and displays the indefinite integral of the entered function
4. Plot the function, its first derivative and its integral [use subplots]
5. Exit

 

Make sure:

Error correcting is needed

Sample runs should be included. [need to cover all possiblities]

The answer

Description:

This MATLAB program presents a menu that allows the user to:

• Enter a symbolic function

• Display the nth derivative (where n = 1, 2, or 3)

• Calculate and display the indefinite integral

• Plot the function, its first derivative, and its integral (with subplots)

• Exit the program

The program includes error checking for invalid input and demonstrates sample runs for all menu options.

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MATLAB Code:

matlab

% Symbolic Function Calculator and Plotter Menu

clc; clear; close all;

syms x;
user_func = [];
func_entered = false;

while true
    disp('====== Symbolic Function Menu ======');
    disp('1. Enter a function in symbolic format');
    disp('2. Display the nth derivative (n = 1, 2, or 3)');
    disp('3. Calculate and display the indefinite integral');
    disp('4. Plot the function, its first derivative and its integral');
    disp('5. Exit');
    choice = input('Select an option (1-5): ');

    switch choice
        case 1
            f_input = input('Enter a function of x (e.g., sin(x), x^3+2*x, exp(-x)): ', 's');
            try
                user_func = str2sym(f_input);
                func_entered = true;
                disp(['Function entered: ', char(user_func)]);
            catch
                disp('Invalid function format! Please try again.');
                func_entered = false;
            end

        case 2
            if ~func_entered
                disp('Please enter a function first (option 1).');
                continue;
            end
            n = input('Enter n for the nth derivative (1, 2, or 3): ');
            if isnumeric(n) && ismember(n, [1 2 3])
                deriv = diff(user_func, x, n);
                disp(['The ', num2str(n), 'th derivative:']);
                pretty(deriv);
            else
                disp('Error: n must be 1, 2, or 3.');
            end

        case 3
            if ~func_entered
                disp('Please enter a function first (option 1).');
                continue;
            end
            integral_result = int(user_func, x);
            disp('The indefinite integral is:');
            pretty(integral_result);

        case 4
            if ~func_entered
                disp('Please enter a function first (option 1).');
                continue;
            end
            d1 = diff(user_func, x, 1);
            integral_result = int(user_func, x);

            fplot(user_func, [-10,10]);
            title('Function');
            subplot(3,1,1);
            fplot(user_func, [-10,10]);
            title('Original Function');
            grid on;

            subplot(3,1,2);
            fplot(d1, [-10,10]);
            title('First Derivative');
            grid on;

            subplot(3,1,3);
            fplot(integral_result, [-10,10]);
            title('Indefinite Integral');
            grid on;

        case 5
            disp('Exiting the program. Goodbye!');
            break;

        otherwise
            disp('Invalid choice. Please select from 1 to 5.');
    end
    disp(' '); % Blank line for readability
end

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Sample Runs:

Sample Run 1: (Try invalid function, then valid one)

====== Symbolic Function Menu ======
1. Enter a function in symbolic format
...
Select an option (1-5): 1
Enter a function of x (e.g., sin(x), x^3+2*x, exp(-x)): sin(x
Invalid function format! Please try again.

Select an option (1-5): 1
Enter a function of x (e.g., sin(x), x^3+2*x, exp(-x)): sin(x)
Function entered: sin(x)

Sample Run 2: (Try derivative before entering function)

Select an option (1-5): 2
Please enter a function first (option 1).

Sample Run 3: (Show 2nd derivative of sin(x))

Select an option (1-5): 2
Enter n for the nth derivative (1, 2, or 3): 2
The 2th derivative:
-sin(x)

Sample Run 4: (Display indefinite integral)

Select an option (1-5): 3
The indefinite integral is:
-cos(x)

Sample Run 5: (Plot function, derivative, and integral)

Select an option (1-5): 4
-- [Shows figure with three subplots: sin(x), cos(x), -cos(x)] --

Sample Run 6: (Exit)

Select an option (1-5): 5
Exiting the program. Goodbye!

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Note:

• The program checks for valid function input and menu choices.

• Derivative order must be 1, 2, or 3.

• The plot option uses subplot to show all curves on the same figure.

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