Gaussian Quadrature

implementation

evaluation

first we need to transform from $[-1,1]$ to $[a,b]$ which required to update points and weights

$$x_i=\frac{b-a}{2}{\xi }_i+\frac{a+b}{2}$$

where $x_i$ is the new mapped point and ${\xi }_i$ is the old one

$$w_i=\frac{b-a}{2}{w}_i$$ $$I={\int }_a^{b}fdx=\sum \frac{b-a}{2}{w}_{i}f(x_i)$$

exact for $n$ node

up to $2n-1$ degree