Abstract:
This paper discusses a technique to estimate an error in numerical integration methods, which is a review and an expansion, as well as partial correction from
the article Peter R. Mercer [The College Mathematics Journal, 36 (2005): 27-34].
After obtaining the error estimates of the numerical integration methods for a single interval, composite error estimate forms are developed, which are only dependent on the first derivatives of the function. By comparing the error estimates obtained
with error estimates obtained by polynomial interpolation error, it is visible that the error estimates obtained for the trapezoidal method and the midpoint method
are sharper. This finding does not apply to the Simpson method.
