Observe the figure :

The engine is approximately above the top of the fuel tank.

Weight of the diesel fuel is approximately .

Since the engine is approximately above the top of the fuel tank the volume can be considered as

Volume, .

The force is calculated by .

The force of pushing one rectangle with depth is .

.

The work done can be calculated by using the formula .

Since the height of the engine is above the top of the fuel tank the limit ranges from to .

.

, so write in the terms of .

Apply integration :

The work done by the fuel pump in raising the fuel tank of fuel to the level of the engine is .