Explanation Given: s ( x ) = 0.01 x ( 6 − x ) g / c m for 0 ≤ x ≤ 6 Calculation: Total mass of the deposit is given by density*length. We have been given that, length of the strip = 6cm and density of deposit = s ( x ) = 0.01 x ( 6 − x ) g / c m which varies from 0 to 6. Therefore, total mass of the deposit, M in g = integral of linear density s(x) g/cm M = ∫ 0 6 s ( x ) d x M = ∫ 0 6 0.01 x ( 6 − x ) d x ∴ M = 0.01 ∫ 0 6 ( 6 x − x 2 ) d x ∴ M = 0.01 [ ∫ 0 6 6 x d x − ∫ 0 6 x 2 d x ] ∴ M = 0...

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.2, Problem 27E

To determine

To find: the total mass of the deposit along the strip of length 6cm, whose density is given by $s (x) = 0.01 x (6 - x) g / c m$ for $0 \leq x \leq 6$

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Chapter 6.2, Problem 26E

Chapter 6.2, Problem 28E

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Chapter 6 Solutions

Calculus - Standalone book

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the total mass of the deposit along the strip of length 6cm, whose density is given by s ( x ) = 0.01 x ( 6 − x ) g / c m for 0 ≤ x ≤ 6

Solution Summary: The author calculates the total mass of the deposit by integrating the density.

Concept explainers

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To find: the total mass of the deposit along the strip of length 6cm, whose density is given by $s (x) = 0.01 x (6 - x) g / c m$ for $0 \leq x \leq 6$

Want to see the full answer?

Chapter 6 Solutions

the total mass of the deposit along the strip of length 6cm, whose density is given by s ( x ) = 0.01 x ( 6 − x ) g / c m for 0 ≤ x ≤ 6

Solution Summary: The author calculates the total mass of the deposit by integrating the density.

Concept explainers

Videos

To find: the total mass of the deposit along the strip of length 6cm, whose density is given by s(x)=0.01x(6−x)g/cm for 0≤x≤6

Want to see the full answer?

Chapter 6 Solutions

To find: the total mass of the deposit along the strip of length 6cm, whose density is given by $s (x) = 0.01 x (6 - x) g / c m$ for $0 \leq x \leq 6$