Solving Work Done in Lifting 150ft Cable, 4lb/ft

[Pruddy]

Homework Statement

Find the work done in winding up a 150 ft cable that weighs 4.00 lb/ft. Assume that the weight includes the gravitational force. In order words exclude the gravitational force g in your calculation.

Homework Equations

W = ∫ pgA(y)D from a ft to b
a = area
P = density
g = gravitational
d= lifting distance

The Attempt at a Solution

The question clearly states that g should be excluded from the equation.
W = ∫A(y) (d) from 150 to zero

But I am not sure of my work.

 

[Pruddy]

Finally found a solution to the problem.
W= ∫ py dy from 0 to 150
p = 4

W = 4∫ ydy
W = 4[y^2/2]
W = 4 [11250] = 45000

I Think this is the right answer to the problem.