Use case
It is an Error correction technique that improves the result of the an Integration by improving the integral itself. (As opposed to doing so through iterations)
Derivation
An integral can be written as
Where Numerical approximation, the truncation error.
Suppose we make to estimates step sizes and and we get the same values for the error.
For the Trapezoid Rule, the error is
Assume is constant regardless of step size. Then the ratio of the errors is given by.
Substitution in eqn.