How did they deduce that this integral is equal to 0

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I don't quite understand the solution to this question, which is :

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What I don't understand is how do they calculate that the joint density integrates to 0? What is the joint density(if there exists one at all) ?

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distribution support should belong to Borel $\sigma$-algebra, thus it should have some area, here support for distribution $(X, Y)$ are only 2 lines which have area of 0 thus integral is = 0