RiemannIntegral: Problem $7$

$(1$ point$)$

Consider the function $f(x)=-\frac{x^2}{2}-4.$

In this problem you will calculate ${\displaystyle \underset{0}{\overset{2}{}}}(-\frac{x^2}{2}-4)dx$ 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$-$interval.

Calculate $R_n$ for $f(x)=-\frac{x^2}{2}-4$ on the interval $0,2$ and write your answer as a function of $n$ without any summation signs.

$R_n=$