Question

Please Use matlab and show command window. Please go through all steps

Using a Dialog button with 3 buttons have the user chose one of the 3 anonymous functions below to be used in the later selected three Programmed functions (1) Integral by Trapezoidal Method,(2) Integral by Simpson Method, or (3) Root by BiSection Method.:

a. f(x) = 2*x^5 -3*x^2 – 5

b. f(x) = x^2 – 5

c. f(x) = x^(1/2)

2. Using an input statement ask the user to pick Midpoint, Simpson, or ROOT. Make sure you are consistent with string or number. You can use what you are comfortable with. The input variable will then be used in a switch case statement. Each case will do the following

a. First case (Midpoint Integral) i. Ask for the three inputs a, b, and n ii. Call the function iii. Use fprintf to output the answer

b. Second case (Simpson Integral) i. Ask for the three inputs a, b, and n ii. Call the function iii. Use fprintf to output the answer

c. Third case (ROOTs) i. Ask for the three inputs a, b, and epsilon the convergence limit ii. Call the function iii. Use fprintf to output the answer

Answer 1

function result = Midpoint(f, a, b, samples)

x = linspace(a,b,samples);

dx = (a-b)/samples;
result = 0;
for i = 1:samples
  
    result = result + f(x(i) + dx)*dx;
end
end

function result = Simpson(f,a,b, samples)

dx = (b-a)/samples;

x= linspace(a,b,samples);

result = 0;

for i = 1:samples
    if i == 1
        result = result + f(x(i));
    else
        if mod(i, 2) == 0
          
            result = result + 4 * f(x(i));
    else
       result = result + 2 * f(x(i));
        end
  
  
    end

end
result = dx / 3 * result;
end

function result = BiSection(f, a, b, epsilon)
  
    t = (a+b)/2;
  
    while (f(t) > epsilon)
      
        if f(t)*f(b) < 0
          
            a = t;
        else
            if f(t) * f(a) < 0
             b = t;
            end
          
        end
        t= (a + b)/2;
      
    end

    result = t;
end

clc
clear

f1 = @(x) 2*x^5 - 3*x^2 - 5;

f2 = @(x) x^2 - 5;

f3 = @(x) x^(1/2);

disp(spaces(10) + "Your choices: ")
disp("Midpoint" + spaces(5) + "Simpson" + spaces(5) + "Bisection")

choice = input();

if (choice == "Midpoint")
    a = input("Input value of a: ", "s");
    a = str2double(a);
  
    b = input("Input value of b: ", "s");
    b = str2double(b);
  
    c = input("Input value of n(number of samples): ", "s");
    c= str2double(c);
  
    result = Midpoint(f1, a, b, n);
    result1 = Midpoint(f2, a, b, n);
    result3 = Midpoint(f3, a, b, n);
  
    disp("Value of integral of 2*x^5 - 3*x^2 - 5 within "+a+" and "+b+" is "+ result)
  
    disp("Value of integral of x^2 - 5 within "+a+" and "+b+" is "+ result1)
  
    disp("Value of integral of x^(1/2) within "+a+" and "+b+" is "+ result2)
  
else
    if choice == "Simpson"
      
    a = input("Input value of a: ", "s");
    a = str2double(a);
  
    b = input("Input value of b: ", "s");
    b = str2double(b);
  
    c = input("Input value of n(number of samples): ", "s");
    c= str2double(c);
  
    result = Simpson(f1, a, b, n);
    result1 = Simpson(f2, a, b, n);
    result3 = Simpson(f3, a, b, n);
  
    disp("Value of integral of 2*x^5 - 3*x^2 - 5 within "+a+" and "+b+" is "+ result)
  
    disp("Value of integral of x^2 - 5 within "+a+" and "+b+" is "+ result1)
  
    disp("Value of integral of x^(1/2) within "+a+" and "+b+" is "+ result2)
      
    else
    a = input("Input value of a: ", "s");
    a = str2double(a);
  
    b = input("Input value of b: ", "s");
    b = str2double(b);
  
    epsilon = input("Input value of epsilon: ", "s");
    epsilon= str2double(epsilon);
  
    result = BiSection(f1, a, b, epsilon);
    result1 = BiSection(f2, a, b, epsilon);
    result3 = BiSection(f3, a, b, epsilon);
  
    disp("Value of integral of 2*x^5 - 3*x^2 - 5 within "+a+" and "+b+" is "+ result)
  
    disp("Value of integral of x^2 - 5 within "+a+" and "+b+" is "+ result1)
  
    disp("Value of integral of x^(1/2) within "+a+" and "+b+" is "+ result2
    end
end