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A trough is 5 meters long and 1 meter high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x from x = -1 to x = 1. The trough is full of water. Find the amount of work (in joules) required to empty the trough by pumping the water over the top. (The acceleration due to gravity is 9.8 and the density of water is 1000 kg m³ m s²

A trough is 5 meters long and 1 meter high. The vertical cross-section of the trough parallel to an end is shaped like the graph of y = x from x = -1 to x = 1. The trough is full of water. Find the amount of work (in joules) required to empty the trough by pumping the water over the top. (The acceleration due to gravity is 9.8 and the density of water is 1000 kg m³ m s²

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A trough is 5 meters long and 1 meter high. The vertical cross-section of the trough parallel to an end is shaped like the graph of \( y = x^6 \) from \( x = -1 \) to \( x = 1 \). The trough is full of water. Find the amount of work (in joules) required to empty the trough by pumping the water over the top. (The acceleration due to gravity is \( 9.8 \, \frac{m}{s^2} \) and the density of water is \( 1000 \, \frac{kg}{m^3} \).)
Transcribed Image Text:A trough is 5 meters long and 1 meter high. The vertical cross-section of the trough parallel to an end is shaped like the graph of \( y = x^6 \) from \( x = -1 \) to \( x = 1 \). The trough is full of water. Find the amount of work (in joules) required to empty the trough by pumping the water over the top. (The acceleration due to gravity is \( 9.8 \, \frac{m}{s^2} \) and the density of water is \( 1000 \, \frac{kg}{m^3} \).)
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