Integrating with a static starting value and changing end value

My code so far is:

Cp= @(T) 0.132+1.56e-4.*T+2.64e-7.*T.^2;
dT=linspace(0,300);
T0=-100;
dH=integral(Cp,T0,dT); %does not work yet
plot(dT,dH)
box on

I was wondering how I can make the integral work for this when T0 is a constant and dT isn't. I have tried using T0=-100*ones(size(dT));, but it didnt help

Answer 1

[Bjorn Gustavsson]

Either you'll have to simply loop:

Cp= @(T) 0.132+1.56e-4.*T+2.64e-7.*T.^2;
dT=linspace(0,300);
T0=-100;
for i_T = numel(dT):-1:1
  dH(i_T)=integral(Cp,T0,dT(i_T)); %does not work yet
end
plot(dT,dH)
box on

or get an analytical solution of the integral (using the symbolic tools in matlab, by hand, or some other means (matematica, tables...)).

If trapz is a good enough way to approximate your integral you could use cumtrapz.

Just for a simple test I wrapped the integral function into a cumintegral function (since the loop recalculates the integrals over the same intervall multiple times I thought there would be some time to gain - but not more than a factor of ~1/2 in my test-case).

HTH