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?Show how to approximate the required work by a Riemann sum. Then express the work as an
Chapter 5, Problem 21(choose chapter or problem)
Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.
An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the fact that the density of water is \(1000 \mathrm{~kg} / \mathrm{m}^{3}\).)
Questions & Answers
QUESTION:
Show how to approximate the required work by a Riemann sum. Then express the work as an integral and evaluate it.
An aquarium 2 m long, 1 m wide, and 1 m deep is full of water. Find the work needed to pump half of the water out of the aquarium. (Use the fact that the density of water is \(1000 \mathrm{~kg} / \mathrm{m}^{3}\).)
ANSWER:Step 1 of 2
Assume the top of the aquarium is at height and the bottom at height .
Then we need to lift the slice at height by meters.