Center of Mass Movement in Work Integration

[Jet1045]

I posted this question in the calculus section but i guess that's the wrong place, so here is my question:

1. Homework Statement

Alright, so my calc class isn't getting easier and we started doing 'work' problems, and I'm just not getting it. Here's the question: A 10ft long weighs 25lbs and hangs from a ceiling. Find the work done in lifting the lower end of the chain to the ceiling so that its level with the upper end.

2. Homework Equations



3. The Attempt at a Solution
Alright, so for the interval of [0,10] you would divide it into n subintervals of length Δx.
The weight of the piece would be (25/10)Δx which is simplified to (5/2)Δx

So in class we did an example similar to this but it only involved lifting the cable to the top of the roof, where as this question you are taking the bottom and lifting it to meet the other end at the roof. So i don't think it is as simple as taking the integral from 0 to 10 of (5/2)x like it is for just lifting a chain to the top of the roof.
ANy help would be greatly appreciated. :)

 

[Spinnor]

Work = mgh,


what distance does the center of mass move? Where is the center of mass before and after the move in relation to the ceiling?