Tyw7 - I notice that there is the following couple of lines of code
while aim < abs_err
goto 2
What is the intent behind this line? There is no goto statement in MATLAB so if you are trying to repeat the block of code that precedes this, you will have to find an alternative.
If you want to change the number of subintervals n until the error falls within the desired tolerance, then you could do something like the following. First, set n as you have done already
%this is the aim of absolute error required
aim = 1e-4;
%define the integration limits
a=0;
b=2;
%define the number of sub-intervals to be used
if nargin == 1
n=N;
else
n=45;
end
Now set up the while loop that will continue approximating the definite integral until the condition has been satisfied
abs_error = realmax;
while abs_error > aim
h=(b-a)/n;
integral=0.0;
for k=1:n
% etc.
end
abs_err=abs(4-integral);
n = n + 1;
end
So on the first iteration of the while loop, we estimate the integral given the chosen n. We calculate the abs_err and increment n so that on subsequent iterations of the loop (if necessary) we can increase the number of subintervals in our interval.
Note that a problem with the above code is that what happens if we never converge to aim. Then we get stuck in the loop and never exit. When using while loops in this manner, it is good practice to include a maximum allowed iterations count so that eventually the loop will terminate when this count has been exceeded.
