(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the integral of the function f(x)=3 when x is rational and 2 when x is irrational on the interval [0,1].

2. Relevant equations

3. The attempt at a solution

So I partition [0,1] into two disjoint sets A and B. [tex]A=[0,1] \cap Q[/tex] and [tex]B=[0,1] \cap Q^{c}[/tex].

Now the integral should be equal to 3 length(A) + 2 length(B). Since A is a countable set then its measure is zero. But I do not understand how to calculate the measure of B since it is uncountable.

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# Homework Help: Integral using Lebesgue Measure

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