Suppose f:[a,b] → R is integrable, f(x) ≥ 0 for all X, and a f> 0. Which of the following is true? We must have f> 0 on [a, b]. There must be at least one point in [a, b] where f>0, but there need not be more than finitely many points where ƒ > 0. There need not be any points in [a,b] where f> 0. O There must be infinitely many points in [a,b] where f> 0, but it need not the case that f>0 everywhere.
Suppose f:[a,b] → R is integrable, f(x) ≥ 0 for all X, and a f> 0. Which of the following is true? We must have f> 0 on [a, b]. There must be at least one point in [a, b] where f>0, but there need not be more than finitely many points where ƒ > 0. There need not be any points in [a,b] where f> 0. O There must be infinitely many points in [a,b] where f> 0, but it need not the case that f>0 everywhere.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.1: Postulates For The Integers (optional)
Problem 29E
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![QUESTION 4
Suppose f:[a,b] → R is integrable, f(x) > 0 for all X, and
b
Sf> 0. Which of the following is true?
a
We must have f> 0 on [a,b].
There must be at least one point in [a, b] where f>0, but there need not be more than finitely many points where f>0.
O There need not be any points in [a,b] where f> 0.
O There must be infinitely many points in [a,b] where f> 0, but it need not the case that f>0 everywhere.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd22a7882-835a-44a8-b8af-d7a415b67cf6%2Ff21a8a15-6d25-4c48-b7b5-e18336cd9b31%2Fugu0fm_processed.png&w=3840&q=75)
Transcribed Image Text:QUESTION 4
Suppose f:[a,b] → R is integrable, f(x) > 0 for all X, and
b
Sf> 0. Which of the following is true?
a
We must have f> 0 on [a,b].
There must be at least one point in [a, b] where f>0, but there need not be more than finitely many points where f>0.
O There need not be any points in [a,b] where f> 0.
O There must be infinitely many points in [a,b] where f> 0, but it need not the case that f>0 everywhere.
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