Use Simpson's Rule with $n=4$ and the given data to estimate

${\displaystyle \underset{7}{\overset{11}{}}}f(x)dx$

Enter an exact value or round your final answer to three decimal places.

$\backslash$table$[[x,7,7\mathrm{.}5,8,8\mathrm{.}5,9,9\mathrm{.}5,10,10\mathrm{.}5,11],[f(x),1\mathrm{.}7,1\mathrm{.}4,1\mathrm{.}8,4\mathrm{.}5,3\mathrm{.}9,3\mathrm{.}6,3\mathrm{.}8,7\mathrm{.}7,4]]$

${\displaystyle \underset{7}{\overset{11}{}}}f(x)dx$~~

$$

By: Dr$.$ Roberto Carlos Toro$-$Rodriguez

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$~~$[f({\stackrel{}{x}}_1)f({\stackrel{}{x}}_2)$ cdots $f({\stackrel{}{x}}_n)]x$

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx$~~$\frac{x}{2}[f(x_0)2f(x_1)2f(x_2)$ cdots $2f(x_{n-1})f(x_n)]$