Implementing Clenshaw-Curtis quadrature, I Methodology and Experience Clenshaw-Curtis quadrature is a particularly important automatic quadrature scheme for a variety of reasons, especially the high accuracy obtained from relatively few integrand values. However, it has received little use because it requires the computation of a cosine transformation and the arithmetic cost of this has been prohibitive. This paper is in two parts; a companion paper, "II Computing the Cosine Transformation," shows that this objection can be overcome by computing the cosine transformation by a modification of the fast Fourier transform algorithm. This first part discusses the strategy and various error estimates, and summarizes experience with a particular implementation of the scheme. CACM May, 1972 Gentleman, W. M. Clenshaw Curtis, numerical integration, automatic quadrature, error estimates, Chebyshev series 5.16 CA720505 JB January 31, 1978 10:05 AM 1982 4 2355 2355 4 2355 2355 4 2355 2355 4 2355 2355 4 2355 2355 4 2355 2355 4 2355 2355 4 2355 2350 4 2355 2350 4 2355 2354 4 2355 2354 4 2355 2354 4 2355 2354 4 2355 1418 5 2355 1521 5 2355 1597 5 2355 1883 5 2355 2040 5 2355 2350 5 2355 2354 5 2355 2355 5 2355 2355 5 2355 2355 5 2355 2640 5 2355 1418 6 2355 1418 6 2355 1521 6 2355 1597 6 2355 1679 6 2355 2350 6 2355 2354 6 2355 2355 6 2355 2355 6 2355 2355 6 2355