xpress the limit as a definite integral on the given interval.

$\underset{n}{lim}{\displaystyle \underset{i=1}{\overset{n}{}}}[2(x_i^{**}{)}^3-4x_i^{**}]x_i,[2,6]$

Consider the following theorem.

If $f$ is integrable on $a,b,$ then ${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx=\underset{n}{lim}{\displaystyle \underset{i=1}{\overset{n}{}}}f(x_i)x,$ where $x=\frac{b-a}{n}$ and $x_i=a+ix.$

Use the given theorem to evaluate the integral.

${\displaystyle \underset{4}{\overset{7}{}}}(8-2x)dx$