Explanation Given: T ( x ) = 40 s i n ( π x 3 ) + 50 , [ t 1 , t 2 ]=[0, 3] Formula used: Average temperature= 1 t 2 − t 1 ∫ t 1 t 2 T ( x ) d x over the time period [ t 1 , t 2 ] Calculation: Average temperature= 1 t 2 − t 1 ∫ t 1 t 2 T ( x ) d x Put t 2 = 3 and t 1 = 0 = 1 3 − 0 ∫ 0 3 ( 40 s i n ( π x 3 ) + 50 ) d x = 1 3 ∫ 0 3 ( 40 s i n ( π x 3 ) d x + 1 3 ∫

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 6.2, Problem 50E

To determine

To find: The average temperature of bar of length 3 m and temperature $T (x) = 40 s i n (\frac{π x}{3}) + 50^{o} C$ along the time interval [0, 3].

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Chapter 6.2, Problem 49E

Chapter 6.2, Problem 51E

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Chapter 6 Solutions

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The average temperature of bar of length 3 m and temperature T ( x ) = 40 s i n ( π x 3 ) + 50 o C along the time interval [0, 3].

Solution Summary: The author explains how to calculate the average temperature of a bar of length 3 m and the formula of integration as well as its rules.

Concept explainers

Videos

To find: The average temperature of bar of length 3 m and temperature $T (x) = 40 s i n (\frac{π x}{3}) + 50^{o} C$ along the time interval [0, 3].

Want to see the full answer?

Chapter 6 Solutions

The average temperature of bar of length 3 m and temperature T ( x ) = 40 s i n ( π x 3 ) + 50 o C along the time interval [0, 3].

Solution Summary: The author explains how to calculate the average temperature of a bar of length 3 m and the formula of integration as well as its rules.

Concept explainers

Videos

To find: The average temperature of bar of length 3 m and temperature T(x)=40sin(πx3)+50oC along the time interval [0, 3].

Want to see the full answer?

Chapter 6 Solutions

To find: The average temperature of bar of length 3 m and temperature $T (x) = 40 s i n (\frac{π x}{3}) + 50^{o} C$ along the time interval [0, 3].