16.1.2 Integrands with weight functions

For integrands with weight functions the algorithms use Clenshaw-Curtis quadrature rules.

A Clenshaw-Curtis rule begins with an n-th order Chebyshev polynomial approximation to the integrand. This polynomial can be integrated exactly to give an approximation to the integral of the original function. The Chebyshev expansion can be extended to higher orders to improve the approximation and provide an estimate of the error.