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An aquarium 3 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 9.8 m/s2 for g and the fact that the density of water is 1,000 kg/m³.) Show how to approximate the required work (in J) by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter x * as x₁.) lim n ( i=1 Express the work (in J) as an integral in terms of x (in m). Evaluate the integral (in J). dx

An aquarium 3 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 9.8 m/s2 for g and the fact that the density of water is 1,000 kg/m³.) Show how to approximate the required work (in J) by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter x * as x₁.) lim n ( i=1 Express the work (in J) as an integral in terms of x (in m). Evaluate the integral (in J). dx

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 57CR
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An aquarium 3 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 9.8 m/s² for g and the fact that the density of water is 1,000 kg/m³.) Show how to approximate the required work (in J) by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter x,* as x₁.) lim n→∞ n i=1 Ax Express the work (in J) as an integral in terms of x (in m). 670 Evaluate the integral (in J). dx
Transcribed Image Text:An aquarium 3 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 9.8 m/s² for g and the fact that the density of water is 1,000 kg/m³.) Show how to approximate the required work (in J) by a Riemann sum. (Let x be the height in meters below the top of the tank. Enter x,* as x₁.) lim n→∞ n i=1 Ax Express the work (in J) as an integral in terms of x (in m). 670 Evaluate the integral (in J). dx
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