# Proof of Newton–Cotes quadrature rules, I guess?

I've been searching for the proof of this formula, I think the main problem is that the book doesn't really give it a name, therefore it's hard to search it up even online. I read the topics suggested by the site while I was asking this question but coulnd't find this exact formula.
Can anyone help me find the proof or suggest some resources where to find it?

• Without knowledge of $\gamma_n$ and/or more context, it is impossible to know. – Yves Daoust Jul 11 '18 at 17:04
• Apparently the theorem in question is for some specific class of quadrature rules because it's not true for all quadrature rules. If you knew the theorem were true for a given quadrature rule, as it is for Gaussian-type rules, it would be a snap to find $k$ and $\gamma_n$. I have never seen a readable proof that the theorem is valid for Simpson's $3/8$ rule athough or course it is. – user5713492 Jul 12 '18 at 0:34