A well is dug in the shape of a rectangular prism. It is 30ft deep and has a base with area of 40ft^2. Assuming that the soil weighs 150 lbs/ft^3, calculate the work W required to raise the soil to ground level.
W = ∫dW
dW = ρ(area)(distance)dx
The Attempt at a Solution
I had dW = ρ40(30-x)dx
Then I said W = 150∫[from 0 to 30] 1200-40x dx
Solved to get 2700000ft/lb, which is wrong. I don't really understand what I did wrong here. Isn't this just like pumping water out of a tank or something?