There is a cylindrical barrel with radius 1 and height 4. It is half full of oil and the oil weights 50lb/ft^3. If we want to pump the oil from the bottom to the top of the barrel, how much work is done?
I made the distance from the top of the barrel to a certain point of the barrel "x" so that the volume of the oil being pumped up is " pi(1)^2*x " and the weight would be 50 times this. The distance that this guy has to travel is "4-x". The limits of the integration I chose was from 2 to 4. I calculated the answer to be 400pi/3 but the actual answer is 300pi.
Can someone help me ?

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work = force times distance

let me see if I recall the formula..

distance moved is from 4-y for any given section;
weight for any given volume is 50 times pir^2

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