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.
$$Volume = (5*4*4) $$
$${\Delta}F = 62.4 * 80 $$
$${\Delta}W = 4992(4-y)$$
$$\int_{0}^{4} 4992(4-y) dy = 0 $$
$$\int_{2}^{4} 4992(4-y) dy = -9984 $$
Best Answer
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.