Demonstration of Gaussian Quadrature
Let us here compare three methods for integrating, namely the trapezoidal rule,
Simpson's method and the Gauss-Legendre approach.
We choose two functions to integrate:
\begin{equation*}
\int_1^{100}\frac{\exp{(-x)}}{x}dx,
\end{equation*}
and
\begin{equation*}
\int_{0}^{3}\frac{1}{2+x^2}dx.
\end{equation*}