A heavy rope, $60$ ft long, weighs $0\mathrm{.}7$ lb$/$ft and hangs over the edge of a building $130$ ft high. $($Let x be the distance in feet below the top of the building. Enter xi$*$ as xi$.)$

$($a$)$ How much work W is done in pulling the rope to the top of the building?

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

lim$$n$$$$

n

$0\mathrm{.}7$xi$$

$$xi $=1$

Express the work as an integral.

$0$

$0\mathrm{.}7$x

$$dx

Evaluate the integral.

ft$-$lb

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

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

lim$$n$$$$

n

$0\mathrm{.}7$xi$$

$$xi $=1$

Express the work as an integral.

$0$

$0\mathrm{.}7$x

$$dx

Evaluate the integral.

ft$-$lb