lurflurf said:n=2
so
a2=1
Gauss Legendre numerical integration is a method used to approximate the definite integral of a function. It involves dividing the interval of integration into smaller subintervals and using a weighted sum of function values at specific points within each subinterval to estimate the integral.
The method works by using a predetermined set of points and weights, known as the Gauss-Legendre quadrature points and weights, within each subinterval. These points and weights are chosen to minimize the error in the approximation. The integral is then estimated by taking the weighted sum of function values at these points within each subinterval.
Gauss Legendre numerical integration is known for its high accuracy and efficiency, making it a popular choice for approximating integrals. It also has a wide range of applicability, as it can be used for both smooth and non-smooth functions.
One limitation of this method is that it can only be used for one-dimensional integrals. It also requires the function to be evaluated at specific points, which can be computationally expensive for functions with a large number of variables.
Gauss Legendre numerical integration is generally considered to be more accurate than other numerical integration methods, such as the trapezoidal rule or Simpson's rule. However, it may not be as efficient for certain types of functions, such as oscillatory or highly irregular functions.