- #1
lmedin02
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Homework Statement
Find the integral of the function f(x)=3 when x is rational and 2 when x is irrational on the interval [0,1].
Homework Equations
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.