The relative accuracy of quadrature formulae of the Cotes' closed type

Quadrature formulae, such as those discovered by Gregory, Newton, Simpson and Cotes, which are derivable by integration of Lagrange’s interpolation formula between definite limits, are classified as Cotes’ Type Formulae. When the functional values at the end –points of the range of integration are used the corresponding formulae are said to be of the ‘closed type’. It is shown that, for closed type formulae, the error due to application of a 2n-strip formula is in general less than that due to a (2n+a) –strip formula over the same range of integration when using the same tabular interval of the argument.