$[\frac{-}{1}$ Points$]$

A heavy rope, $40ft$ long, weighs $0\mathrm{.}7l\frac{b}{f}txbe$ the distance $in$ feet below the

top $of$ the building. Enter $x_i^{*}as{x}_i.Wis$ done $in$ pulling the rope $to$ the top $of$ the building?

Show how $to$ approximate the required work $by$ a Riemann sum.

$\underset{n}{lim}{\displaystyle \underset{i=1}{\overset{n}{}}}(,)x$

Express the work $asan$ integral.

${\displaystyle \underset{0}{\overset{\phantom{}}{}}}(,)dx$

Evaluate the integral.

$ft-lb$

$(b)$ How much work $Wis$ done $in$ pulling half the rope $to$ the top $of$ the building?

Show how $to$ approximate the required work $by$ a Riemann sum.

$\underset{n}{lim}{\displaystyle \underset{i=1}{\overset{n}{}}}(,)x$

Express the work $asan$ integral.

${\displaystyle \underset{0}{\overset{\phantom{}}{}}}(,)dx$

Evaluate the integral.

$ft-lb$