Clenshaw-Curtis quadrature

Clenshaw-Curtis quadrature is a numerical method used to approximate the sum, or integral, of a function over a specific interval. It works by evaluating the function at specific points called Chebyshev nodes, which are strategically spaced to reduce errors. These function values are then combined using weighted averages, based on Chebyshev polynomials, to estimate the total area under the curve. This approach is particularly efficient and accurate for smooth functions, making it useful in computational science and engineering for integrating complex functions where exact calculation is difficult.