For a function f integrable on [a,b], its average value on [a,b], also called its mean, is given by the formula av(f) =- b-a f(x) dx. Do f and the constant function av(f) have a b b the same integral over [a,b]? That is, does av(f) dx = | f(x) dx? Give reasons for your answer. Do f and av(f) have the same integral over [a,b]? Choose the correct answer below. O A. Yes, the function f must equal av(f) for at least one value of x in [a,b]. b b 1 O B. No, since av(f) = f(x) dx, and the integral of f over [a,b] is f(x) dx, the two integrals differ by a factor of f)%3D b-a b-a a a OC. No, only when f is equal to the constant function av(f) are the two integrals equal. b O D. Yes, let f(x) dx = A. Then av(f) = A The integral of this constant over [a,b] is A. b-a

For a function f integrable on [a,b], its average value on [a,b], also called its mean, is given by the formula av(f) =- b-a f(x) dx. Do f and the constant function av(f) have a b b the same integral over [a,b]? That is, does av(f) dx = | f(x) dx? Give reasons for your answer. Do f and av(f) have the same integral over [a,b]? Choose the correct answer below. O A. Yes, the function f must equal av(f) for at least one value of x in [a,b]. b b 1 O B. No, since av(f) = f(x) dx, and the integral of f over [a,b] is f(x) dx, the two integrals differ by a factor of f)%3D b-a b-a a a OC. No, only when f is equal to the constant function av(f) are the two integrals equal. b O D. Yes, let f(x) dx = A. Then av(f) = A The integral of this constant over [a,b] is A. b-a

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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