Integration of function of 3 variables

Hello Everybody, I am trying to integrate a function 'fun' of 3 variables 'x,t,y'. Initially I want to integrate this function with respect to 'x' and 't' over certain range. Then I want to evaluate resultant expression in 'y', at different values of 'y'. The Matlab code that I have written is as follows:

clear all; 

K=44.5;
rho=7850;
Cp=475;
k=K/(rho*Cp);
V=20e-3;
l=12e-3;
L=V*l/k;
q=1e6;
syms x t y
fun=@(x,t,y) ((2*q)./(4*pi*K.*t)).*exp(-((-y+V*t-x).^2)./(4*k.*t));
xmin=-l;
xmax=l;
tmin=0;
tmax=Inf;
funty=int(fun,x,xmin,xmax);
funy=int(funty,t,tmin,tmax);
subs(funy,y,-l)

After running this code, I am not getting any numerical answer. Can somebody please tell me where am I going wrong here? In the end I expect numerical answer around 88. Any help in this matter would be appreciated. Thank you in advance,

Nik

Answer 1

[Star Strider]

The symbolic Math Toolbox prefers symbolic functions, not anonymous functions. Omitting the initial constants:

syms x t y
fun(x,t,y) = ((2*q)./(4*pi*K.*t)).*exp(-((-y+V*t-x).^2)./(4*k.*t));
xmin=-l;
xmax=l;
tmin=0;
tmax=Inf;
funty=int(fun,x,xmin,xmax);
funy=int(funty,t,tmin,tmax);
SymResult = subs(funy,y,-l);
NumResult = vpa(SymResult, 15)

NumResult(y) =
8.53663791307516