$(3$ points$)$ In this problem you will calculate the area between f$($x$)=$x$2$ and the x$-$axis over the interval $[2,9]$ using a limit of right$-$endpoint Riemann sums:

Area$=$limn$$$($k$=1$nf$($xk$)$x$).$

Express the following quantities in terms ofn, the number of rectangles in the Riemann sum, andk, the index for the rectangles in the Riemann sum.

We start by subdividing $[2,9]$ into n equal width subintervals $[$x$0,$x$1],[$x$1,$x$2],...,[$xn$1,$xn$]$ each of width $$x$.$ Express the width of each subinterval $$x in terms of the number of subintervals n$.$

$$x$=$

Find the right endpoints x$1,$x$2,$x$3$ of the first, second, and third subintervals $[$x$0,$x$1],[$x$1,$x$2],[$x$2,$x$3]$ and express your answers in terms of n$.$

x$1,$x$2,$x$3=($Enter a comma separated list.$)$

Find a general expression for the right endpoint xk of the kth subinterval $[$xk$1,$xk$],$ where $1$k$$n$.$ Express your answer in terms of k and n$.$

xk$=$

Find f$($xk$)$ in terms of k and n$.$

f$($xk$)=$

Find f$($xk$)$x in terms of k and n$.$

f$($xk$)$x$=$

Find the value of the right$-$endpoint Riemann sum in terms of n$.$

$$k$=1$nf$($xk$)$x$=$

Find the limit of the right$-$endpoint Riemann sum.

limn$$$($k$=1$nf$($xk$)$x$)=$