# Double integral of piecewise function

Tags: double, function, integral, piecewise
 P: 17 1. The problem statement, all variables and given/known data Let f(x,y)= 1 if x is rational, 2*y if x is irrational Compute both double integrals of f(x,y) over [0,1]x[0,1] 2. Relevant equations 3. The attempt at a solution I'm tempted to say that we can do the dydx integral since when x is rational, integrating y gives squares of area=1 and when x is irrational, we get triangles of area 1, so when we integrate over x, we just get 1. Then, since f(x,y) is bounded, the other integral has the same value. Is this reasoning any good at all, or am I just crazy?
 HW Helper P: 3,309 (disclaimer... I don't know too much about it myself, so apologies if i confuse the issue) but could this have something to do with Lebesgue measure, and one of those sets having Lebesgue measure of zero?
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