 Also, Clenshaw-Curtis shares the properties that Gauss-Legendre quadrature enjoys of convergence for all continuous integrands f and robustness to numerical rounding errors.Clenshaw-Curtis is straightforward to implement in formula_16 time by FFT-based methods.Newton-Cotes quadrature is based on approximating "f" by a polynomial interpolant at equally-spaced points in , and like Clenshaw-Curtis also integrates polynomials of degree up to "n" exactly when given "n" samples.