The total work done to move a block can be determined by integrating force with respect to distance. Calculate approximations for the work to move the block from

$x=0ft$ to $x=8ft.$ Give all answers with three $(3)$ decimal places.

$($a$)$ Use multiple trapezoid rule with $h=8ft.[$a$]$

$($b$)$ Use multiple trapezoid rule with $h=4ft.[$b$]$

$($c$)$ Use multiple trapezoid rule with $h=2ft.[$c$]$

$($d$)$ Use Romberg integration to provide an $O(h^6)$ approximation using the answers from $($a$)-($c$).[$d$]$

Specified Answer for: $a176$

Specified Answer for: $b,416$

Specified Answer for: $c364$

Specified Answer for: $345\mathrm{.}5$