Hello, I have a problem I'm working on and having some problems on how to go about it. Here's the problem:

A rocket weighing 3 tons is filled with 40 tons of liquid fuel. In the initial part of the flight, fuel is burned off at a constant rate of 2 tons per 1000 ft of vertical height. How much work is done in lifting the rocket to 3000 ft?

So far, all I have is the force is 43 tons(?- not sure if this is right). And the limits of integration from 0 to 3000. That is all I have. Any help would be appreciated.

If you need the answer to verify: 120,000 ft-tons.