Could someone tell me what is the error when applying the Gauss Quadrature rule in 2 dimensions? I know that for one dimension the error is
$$\frac{(n!)^{4}}{(2n+1)[(2n)!]^{3}} \cdot f(\xi)^{2n}(b-a)^{2n+1}$$
For some $a< \xi <b$.
On the other hand, what value of $\xi$ should I take between $a$ and $b$ for obtain the error? I imagine the error varies depending on the value $\xi$ that I choose.
Thanks