Chapter 4.3, Problem 73E

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361

Chapter
Section

### Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
ISBN: 9781337275361
Textbook Problem

# Think About It Determine whether the Dirichlet function f ( x ) = { 1 , x       is   rational 0 , x       is   rational   is integrable on the interval [0, 1]. Explain.

To determine

If the Dirichlet function

f(x)={1, x is rational0, x is irrational is integrable on the interval [0,1] or not.

Explanation

Given:

Dirichlet function:

f(x)={1,Â xÂ isÂ rational0,Â xÂ isÂ irrational

For the given function f, x can either be a rational number or an irrational one. As a result, there can be infinite values of x in the interval [0,1] however small it might be

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