I cannot integrate after the summation inside the FOR loop. I want to integrate with respect to x.

clear all;

%syms x tau y;
Bn=[0.535 1.02 1.488 1.955 2.439 3.509 3.996 4.464];
T_inf=15;
To=20;
t=200;
G_11=0;
G_12=0;
G_21=0;
G_22=0;
theta_1=1;
G_110=0;

for i=1:1:8
    A_1n(i) = 1;
    B_1n(i) = -2369.123*Bn(1,i);
    A_2n(i) = sin(2.4618*Bn(1,i))*(sin(1.048*Bn(1,i))-2369.123*Bn(1,i)*cos(1.048*Bn(1,i)))+1.6678*(cos(1.048*Bn(1,i))-2369.123*Bn(1,i)*sin(1.048*Bn(1,i)))*cos(2.4618*Bn(1,i));
    B_2n(i) = -sin(2.4618*Bn(1,i))*(1.6678*cos(1.048*Bn(1,i))-3951.2245*Bn(1,i)*sin(1.048*Bn(1,i)))+cos(2.4618*Bn(1,i))*(sin(1.048*Bn(1,i))-2369.123*Bn(1,i)*cos(1.048*Bn(1,i)));
    
    si_1ns = @(x)((A_1n(i)*sin(Bn(1,i)*x/sqrt(9.1e-5))+B_1n(i)*cos(Bn(1,i)*x/sqrt(9.1e-5))).^2);
%    si_1n =@(x)(A_1n(i)*sin(Bn(1,i)*x/sqrt(9.1e-5))+B_1n(i)*cos(Bn(1,i)*x/sqrt(9.1e-5)));
    si_1nx = @(x)((A_1n(i)*sin(Bn(1,i)*x/sqrt(9.1e-5))+B_1n(i)*cos(Bn(1,i)*x/sqrt(9.1e-5))));
    si_1ny = @(y)((A_1n(i)*sin(Bn(1,i)*y/sqrt(9.1e-5))+B_1n(i)*cos(Bn(1,i)*y/sqrt(9.1e-5))));
    
    si_2ns = @(x)((A_2n(i)*sin(Bn(1,i)*x/sqrt(1.65e-5))+B_2n(i)*cos(Bn(1,i)*x/sqrt(1.65e-5))).^2);
    si_2nx = @(x)((A_2n(i)*sin(Bn(1,i)*x/sqrt(1.65e-5))+B_2n(i)*cos(Bn(1,i)*x/sqrt(1.65e-5))));
%    si_2n = @(x)(A_2n(i)*sin(Bn(1,i)*x/sqrt(1.65e-5))+B_2n(i)*cos(Bn(1,i)*x/sqrt(1.65e-5)));
    si_2ny = @(y)((A_2n(i)*sin(Bn(1,i)*y/sqrt(1.65e-5))+B_2n(i)*cos(Bn(1,i)*y/sqrt(1.65e-5))));
    
    Norm(i) = (226/9.1e-5)*integral(si_1ns,0,0.01)+(57.7/1.65e-5)*integral(si_2ns,0.01,0.02);
    
    G_11 = @(y,tau)G_11 + @(y,tau)exp(-(Bn(i).^2)*(t-tau))*(226/9.1e-5)*(1/Norm(i))*si_1nx*si_1ny;
    G_110 = @(x)(G_110 + (exp(-(Bn(i).^2)*(t))*(226/9.1e-5)*(1/Norm(i))*si_1nx*si_1ny));
    
%    G_12 = @(y,tau)G_12 + exp(-(Bn(i).^2)*(t-tau))*(57.7/1.65e-5)*(1/Norm(i))*si_1nx*si_2ny;
%   G_120 = @(x)G_12 + exp(-(Bn(i).^2)*(t))*(57.7/1.65e-5)*(1/Norm(i))*si_1nx*si_2ny;
    
%    G_21 = @(y,tau)G_11 + exp(-(Bn(i).^2)*(t-tau))*(226/9.1e-5)*(1/Norm(i))*si_2nx*si_1ny;
%    G_210 = @(x)G_11 + exp(-(Bn(i).^2)*(t))*(226/9.1e-5)*(1/Norm(i))*si_2nx*si_1ny;
    
%    G_22 = @(y,tau)G_12 + exp(-(Bn(i).^2)*(t-tau))*(57.7/1.65e-5)*(1/Norm(i))*si_2nx*si_2ny;
%    G_220 = @(x)G_12 + exp(-(Bn(i).^2)*(t))*(57.7/1.65e-5)*(1/Norm(i))*si_2nx*si_2ny; 
end

theta_1=(To-T_inf)*integral(G_110,0,0.01); %+(To-T_inf)*integral(G_120,0.01,0.02)+(1.65e-5/57.7)*integral2(G_12,0.01,0.02,0,200);

Answer 1

[Ameer Hamza]

Although I believe that what you are trying to do, can be done in a much simpler way, it is easier to suggest a solution without seeing the mathematical equations. For your current code, you need to change the following two lines to make it work.

change

G_110=0;

to

G_110=@(x) 0;

and change

G_110 = @(x)(G_110 + (exp(-(Bn(i).^2)*(t))*(226/9.1e-5)*(1/Norm(i))*si_1nx*si_1ny));

to

G_110 = @(x)(G_110(x) + (exp(-(Bn(i).^2)*(t))*(226/9.1e-5)*(1/Norm(i))*si_1nx(x).*si_1ny(x)));

Similar changes need to be made to G_11 if you want to integrate it.