The following code snippet creates an example:
>> myfun = @(x) 3*exp(x)./sqrt(1-x.^2);
>> quad(myfun,0,1)
ans =
9.3132
The function value at the end points are
>> myfun(0)
ans =
3
>> myfun(1)
ans =
Inf
Before beginning the integration, MATLAB checks the end points for infinities. If found, the offending point is purturbed slightly so that it moves away from the singularity.
You can see this by looking at the code for QUAD:
>> edit quad
The code snippet below from QUAD shows how this is done:
% Fudge endpoints to avoid infinities.
if ~isfinite(y(1))
y(1) = f(a+eps(superiorfloat(a,b))*(b-a),varargin{:});
fcnt = fcnt+1;
end
if ~isfinite(y(7))
y(7) = f(b-eps(superiorfloat(a,b))*(b-a),varargin{:});
fcnt = fcnt+1;
end
In the above code snippet, y(1) and y(7) are the interval end points.
