Hi, I need help with this problem:

How much work is done lifting a 15 pound object from the ground to the top of a 55 foot building if the cable used weighs 2.5 pounds per foot?

I tried to solve the problem like this (sorry for the mess, I had to change numbers and didn't want to rewrite the whole thing again).

Is this correct?

Cable = 2:"1 bs / FX W= = Fax ) dx bidg to bott x 2ibe 137 .5 1 15 16) ground 3715 F ( x ) = 1516 + 185 16 - 2.5 1bs / ft 1 52. 5 = 15 - 2 x W = 152.5 (#5 - 2x ) dx 0 152.5 =1#x - 25 x 2 75#5 2 - (15 ( 50 ) 2. ( 50 ) 2 - (0 ) 2 1 1 5 750 - 1250 = 1500 +1 165 12 15 2 5 ( 58 - 25/ 56 2 = 1 52.5 X - 1.25 ( x 2) 152 . 5 ( 5 5 ) - 1/25 ( 55)4 - 8387. 6-2781.25 14604. 25 ff-10