?Show how to approximate the required work by a Riemann sum. Then express the work as an

Chapter 5, Problem 21

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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 \(1000 \mathrm{~kg} / \mathrm{m}^{3}\).)

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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.

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