I need to solve the following TRIPLE INTEGRAL

I need to solve the following triple integral:

The input data are:

np=10;
sigmac=16e6;
tau=0.9;

a=10e-3;
b=10e-3; 
c=5e-3;     
d=5e-3;
e=8e-3;


za=a;
zb=za+b;
zc=zb+c; 
zd=zc+d;
ze=zd+e;

R1=25e-3;
R2=65e-3;
R3=90e-3;


A4d=1.62e-04-9.53e-04i;
B4d=1.03e+12-2.13e+12i;
gamma4=5.90e+02+2.14e+02i;
alfak=550.0686; 
OMEGA=1;

t=10;

and:

I tried to use this code but it gives me some errors:

Xr4=A4d*exp(gamma4*z)+B4d*exp(-gamma4*z);
Jr4=real((Xr4*(1/R)*besselj(np,alfak*R)*exp(1i*np*(theta-OMEGA*t))));
Jtheta4=real((1i*(1/np)*Xr4*(alfak*besselj(np-1,alfak*R)-(np/R)*besselj(np,alfak*R))*exp(1i*np*(theta-OMEGAt))));
   
fun_r= @(R, theta, z) abs(Jr4)^2*R;
fun_theta=@(R, theta, z) abs(Jtheta4)^2*R;

P_4=(1/sigmac)*integral3(fun_r,R1,R2,0,tau,z3,z4)+integral3(fun_theta,R1,R2,0,tau,z3,z4);
P_5=(1/sigmac)*integral3(fun_r,0,R1,0,tau,z3,z4)+integral3(fun_theta,0,R1,0,tau,z3,z4);
P_6=(1/sigmac)*integral3(fun_r,R2,R3,0,tau,z3,z4)+integral3(fun_theta,R2,R3,0,tau,z3,z4);

[Steven Lord]

What is the full and exact text of the error messages you receive when you run your code? Show us all the text displayed in red and/or orange in the Command Window when you run this code.

[Luigi Stragapede]

To be honest if I consider the previous code I have this error:

Undefined function or variable 'z'.

Error in Untitled5 (line 37)
Xr4=A4d*exp(gamma4*z)+B4d*exp(-gamma4*z);

For this reason I have put Jr4 and Jtheta4 directly inside the function handle fun_r and fun_theta. So the new code is:

fun_r= @(R, theta, z) abs(real(((A4d*exp(gamma4*z)+B4d*exp(-gamma4*z))*(1/R)*besselj(np,alfak*R)*exp(1i*np*(theta-OMEGA*t)))))^2*R;
fun_theta=@(R, theta, z) abs(real((1i*(1/np)*(A4d*exp(gamma4*z)+B4d*exp(-gamma4*z))*(alfak*besselj(np-1,alfak*R)-(np/R)*besselj(np,alfak*R))*exp(1i*np*(theta-OMEGA*t)))))^2*R;


P_4=(1/sigmac)*integral3(fun_r,R1,R2,0,tau,z3,z4)+integral3(fun_theta,R1,R2,0,tau,z3,z4);
P_5=(1/sigmac)*integral3(fun_r,0,R1,0,tau,z3,z4)+integral3(fun_theta,0,R1,0,tau,z3,z4);
P_6=(1/sigmac)*integral3(fun_r,R2,R3,0,tau,z3,z4)+integral3(fun_theta,R2,R3,0,tau,z3,z4);

Now the error is:

Error using  / 
Matrix dimensions must agree.

Error in Untitled5>@(R,theta,z)abs(real(((A4d*exp(gamma4*z)+B4d*exp(-gamma4*z))*(1/R)*besselj(np,alfak*R)*exp(1i*np*(theta-OMEGA*t)))))^2*R

Error in integral3>@(y,z)FUN(x(1)*ones(size(z)),y,z) (line 138)
            @(y,z)FUN(x(1)*ones(size(z)),y,z), ...

Error in integral2Calc>integral2t/tensor (line 228)
        Z = FUN(X,Y);  NFE = NFE + 1;

Error in integral2Calc>integral2t (line 55)
[Qsub,esub] = tensor(thetaL,thetaR,phiB,phiT);

Error in integral2Calc (line 9)
    [q,errbnd] = integral2t(fun,xmin,xmax,ymin,ymax,optionstruct);

Error in integral3/innerintegral (line 137)
        Q1 = integral2Calc( ...

Error in integralCalc/iterateScalarValued (line 314)
                fx = FUN(t);

Error in integralCalc/vadapt (line 132)
            [q,errbnd] = iterateScalarValued(u,tinterval,pathlen);

Error in integralCalc (line 75)
        [q,errbnd] = vadapt(@AtoBInvTransform,interval);

Error in integral3 (line 121)
    Q = integralCalc(@innerintegral,xmin,xmax,integralOptions);

Error in Untitled5 (line 48)
P_4=(1/sigmac)*integral3(fun_r,R1,R2,0,tau,z3,z4)+integral3(fun_theta,R1,R2,0,tau,z3,z4);
 

[Luigi Stragapede]

Please, I really don't know how to solve this problem.

[Walter Roberson]

Change all / to ./

Change all ^ to .^

Change all * to .*

[Luigi Stragapede]

ok thanks. It works.