Hi, I need help on a programming project and need two things, a correct coding file and the problem solved by hand.

I have a template made to make the coding easier but **I need you to put in the right numbers where the * are in the template**

**Please provide notes for the mathematical approach (solving by hand)**

Please submit a .m file of the code and a separate file for the handwritten work

Here is the template, fill in the blanks where the * are with the correct value:

% Numerical Integration % --------------------------Function description--------------------------% % central_fc(): Calculates central finite difference % forward_fc(): Calculates forward finite difference % backward_fc(): Calculates backward finite difference % trapezoid(): Integration by using Trapezoidal Rule % simpson(): Integration by using Simpson's 1/3 % ------------------------------------------------------------------------% clc; clear all; % Given data, V V = [4.1 4.7 5.23; 2.2 2.5 2.7; 1.775 1.995 2.125; 1.35 1.49 1.55; 1.1 1.2 1.24; 0.90 0.99 1.03; 0.79 0.87 0.905; 0.68 0.75 0.78; 0.61 0.675 0.7]; % Given data, P P = [5;10;15;20;25;30;35;40;45]; T = 400; % We estimate enthalpy at T = 400 K n = length(P); % length of P col = 2; % column index of V where T = 400 K delT = 50; % temperature increment = 50 K % Calculate derivative of V by calling FD(Finite Differencing)function % dVdT = central_fd(*,*,*); % dVdT = forward_fd(*,*,*); dVdT = backward_fd(*,*,*); % Calculate function to be integrated: [V-T*(dV/dT)] for i = 1:* *(i) = *(*,*) - T*dVdT(*); end % Integrate function B along P H = trapezoid(P,B); % by Trapezoidal rule % H = simpson(P,B); % by Simpson's 1/3 % Print result fprintf('Enthalpy, H = %f\n',H); function [*] = central_fd(*,*,*) % Input % x: given data (9x3) % h: increment (temperature) % c: column index where T = 400 K % Output % dvdt: derivative of v n = height(x); % n = 9 dvdt = zeros(9,1); for i = 1:n dvdt(i) = ( x(i,c+1) - x(i,c-1) ) / ( 2*h ); end end function [*] = forward_fd(*,*,*) % Input % x: given data (9x3) % h: increment (temperature) % c: column index where T = 400 K % Output % dvdt: derivative of v n = height(x); % n = 9 dvdt = zeros(9,1); for i = 1:n dvdt(i) = ( x(i,c+1) - x(i,c) ) / ( h ); end end function [*] = backward_fd(*,*,*) % Input % x: given data (9x3) % h: increment (temperature) % c: column index of x where T = 400 K % Output % dvdt: derivative of v n = height(x); % n = 9 dvdt = zeros(9,1); for i = 1:n dvdt(i) = ( x(i,c) - x(i,c-1) ) / ( h ); end end function [*] = trapezoid(*,*) % Input % p: pressure data % b: function to be integrated [V-T*(dV/dT)] % Output % H: result of integration % ***Note that index of this code starts 1, not 0. n = length(p); N = n-1; % the number of segments % Adding internal values b_sum = 0.0; for j = 2:N b_sum = b_sum + b(j); end H = (p(n)-p(1)) * (b(1) + 2*b_sum + b(n))/(2*N); end function [*] = simpson(*,*) % Input % p: pressure data % b: function to be integrated [V-T*(dV/dT)] % Output % H: result of integration % ***Note that index of this code starts 1, not 0. n = length(p); N = n-1; % the number of segments % Perform summation of values of even index b1_sum = 0.0; for j = 2:2:N b1_sum = b1_sum + b(j); end % Perform summation of values of odd index b2_sum = 0.0; for j = 3:2:N-1 b2_sum = b2_sum + b(j); end H = (p(n)-p(1)) * (b(1) + 4*b1_sum + 2*b2_sum + b(n))/(3*N); end