Difficult integration question

[regularngon]

Homework Statement

Show that the function f : [0,1] × [0,1] → R given by

f(x,y) =

{ 0 if x is irrational, or x is rational and y is irrational
{ 1/q if x is rational, y = p/q with gcd(p,q) = 1

Is integrable and compute the integral.

Homework Equations

The Attempt at a Solution

I know I have to use the fact that Riemann integrability is equivalent to the fact that for every E > 0 there exists a partition P such that U(f,P) - L(f,P) < E.

Due to the density of the rationals in the reals, we are always going to have L(f,P) = 0. So I just have to find a partition P such that U(f,P) < E. So I'm quite sure that I'm going to have to use the infinite sum of 1/2^n. However, I'm quite stuck on figuring out a valid partition. The more I think, the harder finding this partition seems to be :(

Any suggestions? Thanks.

 

[regularngon]

No one has any suggestions?

 

[MadHawk]

The first condition of this question is similar to that of Drichilet function. Break the condition further from this.