Question

Error calculation in trapezoidal integration

Answer 1

If you know the true area then compute the error by direct subtraction. If you don't know the true area -- i.e., because you have the continuous form of the function y=f(x), but it cannot be analytically integrated, -- then you could take finer and finer samplings of the function and see what trapz(y,x) converges to. Then, use that as an estimate of the true area.If you know bounds on the derivatives of f(x), you could use error estimation formulas from here.If you don't know anything about the continuous form of the function you're integrating, then what notion of "error" are you using?