Consider the function $f(x)=\frac{x^2}{3}-8.$

In this problem you will calculate ${\displaystyle \underset{0}{\overset{4}{}}}(\frac{x^2}{3}-8)dx$ by using the definition

${\displaystyle \underset{a}{\overset{b}{}}}f(x)dx=\underset{n}{lim}[{\displaystyle \underset{i=1}{\overset{n}{}}}f(x_i)x]$

The summation inside the brackets is $R_n$ which is the Riemann sum where the sample points are chosen to be the right$-$hand endpoints of each sub$-$i Calculate $R_n$ and write your answer as a function of $n$ without any summation signs.

$R_n=1$

$\underset{n}{lim}{R}_n=$