find the work done in winding up a 175 ft cable that weighs 4.00 lb/ft?

Answer 1

Assuming the whole cable is just hanging there, the work required to raise it up is

∫(175-x)(4dx)[0,175]
= 4(175x - .5x^2)[0,175]
= 700x - 2x^2[0,175]
= [700*175 - 2*175^2] - [0-0]
= 61250

Answer 2

61250