Let $\backslash ($ f$($x$)=2$ x$^\{2\}\backslash )$ be defined on the interval $\backslash ([-2,1]\backslash ).$

$($a$)$ Approximate the area under the curve of the function using three rectangles and right endpoints.

$($b$)$ Approximate the area under the curve of the function using three rectangles and left endpoints.

$($c$)$ Write a formula for $\backslash ($ R$\_\{$n$\}\backslash ),$ the estimate using $\backslash ($ n $\backslash )$ rectangles and right endpoints, as a summation of $\backslash ($ n $\backslash )$ terms.

$($d$)$ Use your answer in part $($c$)$ to find a closed$-$form formula for $\backslash ($ R$\_\{$n$\}\backslash ).($This formula should not have a summation sign or be given as a sum of $\backslash ($ n $\backslash )$ terms.$)$

$($e$)$ Use the formula in part $($c$)$ to compute the area exactly.