The exact results is $2.11450175075....$. With just two mesh points we recall from the previous subsection that $\omega_1=\omega_2=1$ and that the mesh points are the zeros of $L_2(x)$, namely $x_1=-1/\sqrt{3}$ and $x_2=1/\sqrt{3}$. Setting $N=2$ and inserting these values in the last equation gives $$\begin{equation*} I_2(x=0)=\sqrt{3}\left(e^{1/\sqrt{3}}-e^{-1/\sqrt{3}}\right)=2.1129772845. \end{equation*}$$ With six mesh points we get even the exact result to the tenth digit $$\begin{equation*} I_6(x=0)=2.11450175075! \end{equation*}$$