# Zeros from Trapz integration

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Brittany Burns on 20 Apr 2022
Edited: Torsten on 17 May 2022
I'm trying to solve for Tstar via integration of Dm; however, I keep getting all zeroes. How should I be using trapz? Is it better to use another command?
clear all;clc
%Given
TL=300; %surface T [K]
alpha=4/1000^2; %Thermal diffusivity [m^2/s]
L=2; %thickness [m]
x=0:0.01:L; %[m]
xstar=x/L;
t=[0 2 20 200]*3600; %time [s]
tstar=(alpha.*t)/L^2;
%Temperatures
T0x0=340;%T0(x=0)
T0x=-182.22.*x.^3 + 582.22.*x.^2 - 445.56.*x + 340; %To(x)
T0star = (T0x - TL)./(T0x0 - TL); %T0 star
for k = 1:length(t)
for i = 1 : length(x)
lambda(i) = ((2*i - 1)*pi) / 2;
fun(i,k)=T0star(i).*cos(lambda(i).*xstar(i));
Dm(i,k)=trapz(fun(i,k),0,1);
Tstar(i,k)=Dm(i,k)*cos(lambda(i)*xstar(i))*exp(-(lambda(i))^2*tstar(k));
end
end
##### 2 CommentsShowHide 1 older comment
John D'Errico on 17 May 2022
It looks like you think that trapz is a tool that can do intgration over an interval. For example you call trapz with THREE arguments. For example, when I do this:
trapz(5,0,1)
ans = 0
As you should see, trapz returns zero. Why? trapz is not integrating the constant function with value 5, over the interval [0,1]. Instead, what you did just misuses trapz. Read the help for trapz. Look at the examples of use.

Torsten on 17 May 2022
Edited: Torsten on 17 May 2022
Maybe you mean something like
L = 2; %thickness [m]
TL = 300; %surface T [K]
T0x0 = 340;%T0(x=0)
T0x = @(x) -182.22.*x.^3 + 582.22.*x.^2 - 445.56.*x + 340;
T0star = @(x) (T0x(x) - TL)./(T0x0 - TL); %T0 star
fun = @(x,i) T0star(x).*cos((2*i-1)/2 * pi * x/L);
x = 0:0.01:L; %[m]
I = 1:numel(x);
value = arrayfun(@(i)integral(@(x)fun(x,i),0,L),I)

R2022a

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