To find the average value of a function g(x) over the interval [a,b] you need to: Take the limit of a Riemann sum as n grows without bounds. Calculate the total area enclosed between the curve g(x) and the x-axis. Calculate the value of the definite integral of g(x) from x=a to x=b, and then divide this value by the length of the interval (b-a). Add the values of g(a) and g(b), and divide the result by 2.
To find the average value of a function g(x) over the interval [a,b] you need to: Take the limit of a Riemann sum as n grows without bounds. Calculate the total area enclosed between the curve g(x) and the x-axis. Calculate the value of the definite integral of g(x) from x=a to x=b, and then divide this value by the length of the interval (b-a). Add the values of g(a) and g(b), and divide the result by 2.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
ChapterA: Appendix
SectionA.2: Geometric Constructions
Problem 10P: A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in...
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![To find the average value of a function g(x) over the interval [a,b] you need to:
Take the limit of a Riemann sum as n grows without bounds.
Calculate the total area enclosed between the curve g(x) and the x-axis.
Calculate the value of the definite integral of g(x) from x-a to x=b, and then divide this value by the length of
the interval (b-a).
Add the values of g(a) and g(b), and divide the result by 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F411b6511-1b12-4b78-aa94-8e8cabb84738%2F0043eb20-7852-4565-b129-3ac9e538ff65%2F2p8q5dn_processed.png&w=3840&q=75)
Transcribed Image Text:To find the average value of a function g(x) over the interval [a,b] you need to:
Take the limit of a Riemann sum as n grows without bounds.
Calculate the total area enclosed between the curve g(x) and the x-axis.
Calculate the value of the definite integral of g(x) from x-a to x=b, and then divide this value by the length of
the interval (b-a).
Add the values of g(a) and g(b), and divide the result by 2.
Transcribed Image Text:If x is measured in months where x=0 represents January of 2000, and F(x) represents the US GDP measured in
millions of dollars, what are the units for f(x) = F'(x), the rate of change of the GDP?
Millions of dollars per month.
Years passed since January of 2000.
Cents per second.
Billions of dollars.
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