(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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# Double integral of piecewise function

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