Recall that Simpson's rule for single variable integrals is a weighted average of two part midpoint rule and one part trapezoid rule. Now meet Dimpson's rule, which is one part midpoint rule and two parts trapezoid rule. If the formula for Dimpson's rule with the usual notation is $\backslash ($ D S$\_\{2$ n$\}=\backslash$frac$\{$h$\}\{3\}\backslash$cdot $\backslash$operatorname$\{$sum$\}($w $.*$ y$)\backslash )$ what is the form of the weight array $\backslash ($ w $\backslash )?$ Prepare a complete solution for this quesiton with explanations on paper by hand and upload pictures below.