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What is the average value of f(x) between x = 1 and x = 5 forf (x) = 2.t? 32 O 31 O 10.82 9.28

What is the average value of f(x) between x = 1 and x = 5 forf (x) = 2.t? 32 O 31 O 10.82 9.28

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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### Average Value of f(x) #### Question: What is the average value of \( f(x) \) between \( x = 1 \) and \( x = 5 \) for \( f(x) = 2^x \)? #### Options: - ○ 32 - ○ 31 - ○ 10.82 - ○ 9.28 To solve this, you need to find the average value of the function over the interval \([1,5]\). The average value of a continuous function \( f(x) \) over the interval \([a,b]\) is given by: \[ \text{Average value} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx \] In this case, \( a = 1 \), \( b = 5 \), and \( f(x) = 2^x \). Therefore, you would compute: \[ \text{Average value} = \frac{1}{5-1} \int_{1}^{5} 2^x \, dx \] After evaluating the integral and simplifying, you'll obtain the average value.
Transcribed Image Text:### Average Value of f(x) #### Question: What is the average value of \( f(x) \) between \( x = 1 \) and \( x = 5 \) for \( f(x) = 2^x \)? #### Options: - ○ 32 - ○ 31 - ○ 10.82 - ○ 9.28 To solve this, you need to find the average value of the function over the interval \([1,5]\). The average value of a continuous function \( f(x) \) over the interval \([a,b]\) is given by: \[ \text{Average value} = \frac{1}{b-a} \int_{a}^{b} f(x) \, dx \] In this case, \( a = 1 \), \( b = 5 \), and \( f(x) = 2^x \). Therefore, you would compute: \[ \text{Average value} = \frac{1}{5-1} \int_{1}^{5} 2^x \, dx \] After evaluating the integral and simplifying, you'll obtain the average value.
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