Calculating Work, pumping water out of a tank, calculus 2 tutorial, application of integration  Summary and Q&A
TL;DR
Calculate the work required to pump all the water in the tank using the formula force times distance.
Questions & Answers
Q: How is the work required to pump all the water in the tank calculated?
The work is calculated by considering the volume of each slice of water and multiplying it by the distance that needs to be pumped for each slice. These values are integrated over the entire height of the tank to obtain the total work.
Q: What are the factors considered when determining the volume of each slice?
The volume of each slice is determined by the length, height, and thickness of the slice. The length and thickness are constant, while the height varies for each slice.
Q: How is the distance to be pumped determined for each slice?
The distance that needs to be pumped for each slice is calculated by subtracting the height of the slice from the total height of the tank and adding any additional distance required to reach the top of the tank.
Q: What is the unit of measurement for the work calculated?
The unit of measurement for the work calculated is Joules (J).
Summary & Key Takeaways

The work required to pump all the water in the tank is calculated by considering slices of the tank and finding the volume of each slice.

The volume of each slice is determined by the length, height, and thickness of the slice.

The distance that needs to be pumped is calculated by considering the height of the slice and the remaining distance to the top of the tank.