Explanation Given: p ( x ) = 10 ( x + 1 ) − 2 k g / m for 0 ≤ x ≤ 1 Calculation: Total mass of the rod is given by Linear density*length. We have been given that, length of rod = 1m and linear density of rod = p ( x ) = 10 ( x + 1 ) − 2 k g / m which varies from 0 to 1. Therefore, total mass of the rod, M in kg = integral of linear density p(x) kg/m M = ∫ 0 1 p ( x ) d x M = ∫ 0 1 10 ( x + 1 ) − 2 d x M = 10 ∫ 0 1 ( x + 1 ) − 2 d x L e t , u = x + 1 ∴ d u = d x ∴ M = 10 ∫ 0 1 u − 2 d u

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 6.2, Problem 25E

To determine

To find: the total mass of a 1-m rod whose linear density function is $p (x) = 10 {(x + 1)}^{- 2} k g / m$ for $0 \leq x \leq 1$

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Chapter 6.2, Problem 24E

Chapter 6.2, Problem 26E

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Chapter 6 Solutions

Calculus - Standalone book

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the total mass of a 1-m rod whose linear density function is p ( x ) = 10 ( x + 1 ) − 2 k g / m for 0 ≤ x ≤ 1

Solution Summary: The author calculates the total mass of a 1-m rod whose linear density function is p ( x ) = 10 (x + 1) 2 k g / m which varies from 0

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To find: the total mass of a 1-m rod whose linear density function is $p (x) = 10 {(x + 1)}^{- 2} k g / m$ for $0 \leq x \leq 1$

Want to see the full answer?

Chapter 6 Solutions

the total mass of a 1-m rod whose linear density function is p ( x ) = 10 ( x + 1 ) − 2 k g / m for 0 ≤ x ≤ 1

Solution Summary: The author calculates the total mass of a 1-m rod whose linear density function is p ( x ) = 10 (x + 1) 2 k g / m which varies from 0

Concept explainers

Videos

To find: the total mass of a 1-m rod whose linear density function is p(x)=10(x+1)−2kg/m for 0≤x≤1

Want to see the full answer?

Chapter 6 Solutions

To find: the total mass of a 1-m rod whose linear density function is $p (x) = 10 {(x + 1)}^{- 2} k g / m$ for $0 \leq x \leq 1$