On the method for numerical integration of Clenshaw and Curtis

Letf(x) be a function, defined and well behaved on the finite intervalaxbClenshaw andCurtis [1] have given a method for the numerical integration off(x) froma tob, based on the approximation off(x) with a finite series of Chebyshev polynomials. We show that this method is asymptotically equivalent to using the trapezoïdal rule for integratingg(y)=f(cosy).