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Let f : [a, b] R be a continuous function on [a, b). Prove that if |f(x)| dx = 0 then f(r) = 0 for all r E [a, b).

Let f : [a, b] R be a continuous function on [a, b). Prove that if |f(x)| dx = 0 then f(r) = 0 for all r E [a, b).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.4: Ordered Integral Domains
Problem 8E: If x and y are elements of an ordered integral domain D, prove the following inequalities. a....
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Let f : [a, b] –R be a continuous function on [a, b). Prove that if |f (r)| dx = 0 then f(r) = 0 for all r E [a, b).
Transcribed Image Text:Let f : [a, b] –R be a continuous function on [a, b). Prove that if |f (r)| dx = 0 then f(r) = 0 for all r E [a, b).
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