Editing Newton–Cotes formulas (section)

== Open Newton–Cotes formulas ==
This table lists some of the Newton–Cotes formulas of the open type. For <math>0 \le i \le n</math>, let <math>x_i = a + (i + 1)h</math> where <math>h = \frac{b - a}{n + 2}</math>, and <math>f_i = f(x_i)</math>.

{|class="wikitable" style="margin:1em auto 1em auto; text-align: center;"
|+'''Open Newton–Cotes Formulas'''
!{{mvar|n}} !!Step size {{mvar|h}} !!Common name !!Formula !!Error term
|-
|0 ||<math>\frac{b - a}{2}</math> ||[[Rectangle method|Rectangle rule]], or<br />midpoint rule ||<math>2hf_0</math> ||<math>\frac{1}{3} h^3f^{(2)}(\xi)</math>
|-
|1 ||<math>\frac{b - a}{3}</math> || ||<math>\frac{3}{2} h(f_0 + f_1)</math> ||<math>\frac{3}{4}h^3f^{(2)}(\xi) </math>
|-
|2 ||<math>\frac{b - a}{4}</math> ||Milne's rule ||<math>\frac{4}{3} h(2f_0 - f_1 + 2f_2)</math> ||<math>\frac{14}{45} h^5f^{(4)}(\xi)</math>
|-
|3 ||<math>\frac{b - a}{5}</math> || ||<math>\frac{5}{24} h(11f_0 + f_1 + f_2 + 11f_3)</math> ||<math>\frac{95}{144} h^5f^{(4)}(\xi)</math>
|}