Error Estimation in the Clenshaw-Curtis Quadrature Formula

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Abstract
Several error estimates for the Clenshaw–Curtis quadrature formula are compared. Amongst these is one which is not unrealistically large, but which is easy to compute and reliable when certain conditions are satisfied. The form of this new error estimate helps explain the considerable accuracy of the Clenshaw–Curtis method when the integrand is well behaved; in this case the method is nearly as accurate as Gaussian quadratures. It is argued that the Clenshaw–Curtis method is a better method for evaluating such integrals than either Romberg's process or Gaussian quadratures.

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