Show that the Dirichlet function f defined on [0 , 1] by f(x) = { 1 if x is rational 0 if x is irrational is not Riemann integrable on [0 ,

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 58E
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Show that the Dirichlet function f defined on [0 , 1] by f(x) = {
1 if x is rational
0 if x is irrational
is not Riemann integrable on [0 , 1]

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