# MATLAB: Problem with integral2 function in the codes

## MATLAB: Problem with integral2 function in the codes

MATLABnumerical integration

integral2 function does not work proberly in my case. How can I simplify the expression in int5=integral2(ht,0,(2*L2),0,L1,’RelTol’,1e-12,’AbsTol’,1e-14,’Method’,’iterated’); and make the code work? Any help is appreciated.
For details, my codes are:
``format longclear allclose allclcsyms xsyms y%syms tq=0.2; %W/cm2a=0.25; %cmL1=0.5; %cmL2=1.5; %cmh=0.001; %W/cm2.Kk=0.011; %W/cm.KT_ambient=23;T_initial=T_ambient;alpha=0.0005789;%k/ro*cdelt=0.0220; %delt stands for deltatime<=(delx^2)/2alfa    Ts=1;T=0;for i=1:10lambda=(i*pi)/(2*L2);int1=integral(@(x)(q*cos(lambda*x)),L2-a,L2+a);int2=integral(@(x)((cos(lambda*x)).^2),L2-a,L2+a);Cn=int1./int2;A2B1=-Cn./(k*lambda);p1=(k.*lambda.*cosh(lambda.*L1))+(h.*sinh(lambda.*L1));p2=(h.*cosh(lambda.*L1))+(k.*lambda.*sinh(lambda.*L1));B3=p1./p2;T=T+(A2B1.*cos(lambda.*x)).*(sinh(lambda.*y)-B3.*cosh(lambda.*y));endtheta=0+T_initial;for t=1:Ts    for m=1:5            mu=(m*pi)/(2*L2);                for n=1:5            beta=-662.09*n+3755.8;            int3=integral(@(x)(cos(mu.*x).^2),0,2*L2);            int4=integral(@(y)(cos(beta.*y).^2),0,L1);            ht=matlabFunction(-T.*cos(mu.*x)*cos(beta.*y));            int5=integral2(ht,0,(2*L2),0,L1,'RelTol',1e-12,'AbsTol',1e-14,'Method','iterated');            Fmn=int5/(int3*int4);            theta=theta+(Fmn.*cos(mu.*x)*cos(beta.*y)*exp(-alpha*(mu.^2+beta.^2).*t));        end    end    figure    ezcontourf(theta+T,[0 3],[0 0.5]);    xlabel('x [cm]')    ylabel('y [cm]')    title('Temperature Distribution [C]')end``

``ht = @(x,y)cos(x.*pi.*(1.0./3.0)).*cos(y.*2.43162e3).*(cos(x.*pi.*(5.0./3.0)).*(cosh(y.*pi.*(5.0./3.0)).*1.010332969266712-sinh(y.*pi.*(5.0./3.0))).*6.32895191273502e-16-cos(x.*pi.*(8.0./3.0)).*(cosh(y.*pi.*(8.0./3.0)).*1.000450157978233-sinh(y.*pi.*(8.0./3.0))).*2.262610130858262-cos(x.*pi.*(4.0./3.0)).*(cosh(y.*pi.*(4.0./3.0)).*1.029468631679565-sinh(y.*pi.*(4.0./3.0))).*5.079090139740538+cos(x.*pi).*(cosh(y.*pi).*1.085034525163738-sinh(y.*pi)).*5.52568847333794e-15+cos(x.*pi.*(1.0e1./3.0)).*(cosh(y.*pi.*(1.0e1./3.0)).*1.000055664759626-sinh(y.*pi.*(1.0e1./3.0))).*7.94622746325111e-1+cos(x.*pi.*(7.0./3.0)).*(cosh(y.*pi.*(7.0./3.0)).*1.001279352938934-sinh(y.*pi.*(7.0./3.0))).*2.290646007531096e-15+cos(x.*pi.*(2.0./3.0)).*(cosh(y.*pi.*(2.0./3.0)).*1.254534770465853-sinh(y.*pi.*(2.0./3.0))).*9.074926360779978-cos(x.*pi.*(1.0./3.0)).*(cosh(y.*pi.*(1.0./3.0)).*1.836310670638647-sinh(y.*pi.*(1.0./3.0))).*1.395001209824949e-13-cos(x.*pi.*3.0).*(cosh(y.*pi.*3.0).*1.000158327683549-sinh(y.*pi.*3.0)).*5.797477778816949e-16+cos(x.*pi.*2.0).*(cosh(y.*pi.*2.0).*1.003634943955502-sinh(y.*pi.*2.0)).*3.684406677903193);x = linspace(0, 3.0, 50);y = linspace(0, 0.5, 50);[X,Y] = meshgrid(x,y);figure(2)meshc(X, Y, ht(X, Y))grid on``