Solution (source code)

= Solution

At $q=3$,
$$
\boxed{Q(g)=\frac{1+1/2}{36}=\frac1{24}=I(g).}
$$
The $y$ factor is now a <cubic polynomial>. <Simpson's rule> still integrates it exactly because its <degree of precision of a quadrature rule> is three. Exactness of <tensor-product quadrature> depends on the <polynomial degree> in each variable, rather than their sum.