Consider the function ƒ : R → R defined by 1 if x #0 if x = 0. f(x) Is f Riemann integrable on [-1, 1]? Justify your answer rigorously using the definition of the Riemann integral.

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 5E: 5. Prove that the equation has no solution in an ordered integral domain.
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Consider the function f : R → R defined by
f(x) =
=
1
0
if x ‡ 0
if x
0.
=
Is f Riemann integrable on [-1, 1]? Justify your answer rigorously using the
definition of the Riemann integral.
Transcribed Image Text:Consider the function f : R → R defined by f(x) = = 1 0 if x ‡ 0 if x 0. = Is f Riemann integrable on [-1, 1]? Justify your answer rigorously using the definition of the Riemann integral.
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How do I prove the statement?

f is Riemann integrable iff f is bounded and f has finite set of discontinuous points.

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