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# Double integral watch

1. I have an answer involving and I assume the condition on f means that this is 0, but I don't see how.

Spoiler:
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What I've done so far:
Write
Reversing order of integration gives
2. (Original post by solC)
I have an answer involving and I assume the condition on f means that this is 0, but I don't see how.
Can't help with the general question.

But i notice that if we let f(x)=sin(x), then this meets the criteria of the question, and doesn't exist, let alone equal zero.
3. Replacing by N (in other words, using your argument, but with a finite upper limit that we will later let go to infinity) , you have

But (*) (by the linear sub x = Ny).

The given condition on existing is enough to show that (*) goes to 0 as N goes to infinity.
4. (Original post by solC)

I have an answer involving and I assume the condition on f means that this is 0, but I don't see how.

Spoiler:
Show

What I've done so far:
Write
Reversing order of integration gives

Would love to know where you got this question from
5. (Original post by DFranklin)
Replacing by N (in other words, using your argument, but with a finite upper limit that we will later let go to infinity) , you have

But (*) (by the linear sub x = Ny).

The given condition on existing is enough to show that (*) goes to 0 as N goes to infinity.
I see, thank you.

(Original post by Lord Nutter)
Would love to know where you got this question from
This was from an example sheet (Vector Calculus).

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