How much work is done in pumping water out over the top edge in order to empty (a) half the tank (b) all of the tank. Rectangular tank is base of 4 feet by 5 feet and a height of 4 feet that is full of water. The water weighs 62.4 pounds per cubic foot. 
This is what I got.
$$Volume = (5*4*4) $$
$${\Delta}F = 62.4 * 80 $$
$${\Delta}W = 4992(4-y)$$
$$\int_{0}^{4} 4992(4-y) dy = 0 $$
$$\int_{2}^{4} 4992(4-y) dy = -9984 $$

You should just change your $\Delta F$.
$$\Delta F = 62.4 \cdot 5\cdot 4 \cdot \Delta y$$
$$\Delta W = 62.4 \cdot 5\cdot 4 \cdot (4-y) \Delta y $$
Then you can set up your definite integral accordingly.
