How do fix this code to give me the error?

%% dt=10
h=10;
t=[100:h:1500];
Cp=(.00000000747989.*t.^3)-(.000028903.*t.^2)+.0423484.*t+36.1064;
dH=trapz(t,Cp)

dH = 7.4939e+04

for i=1:5
    h=h*10;
    tt=100:h:1500;
    CcPp=(.00000000747989.*tt.^3)-(.000028903.*tt.^2)+.0423484.*tt+36.1064;
    aa=trapz(tt,CcPp);
    dHH(i)=aa;
    error(i)=abs((dH-dHH(i))/dH);
    hh(i)=h;
end

Error using matlab.internal.math.getdimarg
Dimension argument must be a positive integer scalar within indexing range.

Error in trapz>getDimArg (line 90)
dim = matlab.internal.math.getdimarg(dim);

Error in trapz (line 44)
dim = min(ndims(y)+1, getDimArg(dim));

[10 dH 0;hh' dHH' error']

plot(log10(hh),log10(error),'o')
xlabel('Log_{10} (\Delta h)')
ylabel('Log_{10} \epsilon')

a=polyfit(log10(hh),log10(error),1);
f=@(x) a(1)*x+a(2);
hold on
fplot(f,[-5 -1])
hold off
a
%%  dt=20
t=[100:20:1500];
Cp=(.00000000747989.*t.^3)-(.000028903.*t.^2)+.0423484.*t+36.1064;
enthalpy_change=trapz(t,Cp)
%% dt=50
t=[100:50:1500];
Cp=(.00000000747989.*t.^3)-(.000028903.*t.^2)+.0423484.*t+36.1064;
enthalpy_change=trapz(t,Cp)
%% dt=100
t=[100:100:1500];
Cp=(.00000000747989.*t.^3)-(.000028903.*t.^2)+.0423484.*t+36.1064;
enthalpy_change=trapz(t,Cp)
%% dt=200
t=[100:200:1500];
Cp=(.00000000747989.*t.^3)-(.000028903.*t.^2)+.0423484.*t+36.1064;
enthalpy_change=trapz(t,Cp)

Answer 1

[Torsten]

Cp = @(T) .00000000747989.*T.^3-.000028903.*T.^2+.0423484.*T+36.1064;
H = @(T) 1/4*.00000000747989.*T.^4-1/3*.000028903.*T.^3+1/2*.0423484.*T.^2+36.1064*T;
deltaT = [10 20 50 100 200];
Tstart = 100;
Tend = 1500;
deltaH_true = H(Tend)-H(Tstart);
for i = 1:numel(deltaT)
  dT = deltaT(i);
  T = Tstart:dT:Tend;
  deltaH(i) = trapz(T,Cp(T));
  error(i) = abs((deltaH(i)-deltaH_true)/deltaH_true);
end
format long
error

error = 1×5

0.000003409811578 0.000013639246313 0.000085245289456 0.000340981157826 0.001363924631303

p = polyfit(log10(deltaT),log10(error),1)

p = 1×2

1.999999999992101 -7.467269618875773

Answer 2

[Walter Roberson]

    h=h*10;
    tt=100:h:1500;
    CcPp=(.00000000747989.*tt.^3)-(.000028903.*tt.^2)+.0423484.*tt+36.1064;
    aa=trapz(tt,CcPp);

What is happening is that your increment gets large enough that eventually tt becomes a scalar. But when you pass a scalar to the second parameter of trapz then it is interpreted as a dimension number rather than as a coordinate. (Note that trapz() of a scalar is 0)