Clenshaw-Curtis integration

Clenshaw-Curtis integration is a numerical method for approximating the area under a curve by evaluating the function at specific points called Chebyshev nodes. These nodes are spaced more densely near the endpoints, improving accuracy for complex functions. The method uses special polynomials, Chebyshev polynomials, to interpolate the function between these points, simplifying the calculation of the integral. Essentially, it approximates the integral by converting the problem into a weighted sum of function values, leveraging the properties of Chebyshev polynomials to achieve efficient and accurate results, especially for smooth functions.