Proper mathematical notation in regarding integrals

[Niles]

Hi

I have a question regarding notation. I have a function f(x, y), which I would like to integrate as
$$\int_{x>0,y<x\frac{1}{\sqrt{\pi}}+1}{f(x, y) dxdy}$$
My question is very simple, and probably very silly: What there a notation which enables me to write the condition for the integral (x>0, y ...) in a much shorter version? I thought about defining a set myself called α, which is defined by this condition and then just write
$$\int_{\alpha}{f(x, y) dxdy}$$
But I am not sure if I am allowed to do this. Even if I am allowed to do this, I don't know how to properly define the set. I would be very happy to receive some professional help.

Best wishes,
Niles.

 

[tiny-tim]

Hi Niles!

You can either write it with two ∫ signs …
$$\int_{x>0}\int_{y<x\frac{1}{\sqrt{\pi}}+1}f(x, y) dxdy$$

or you can write it
$$\int_A f(x, y) dxdy$$

and state separately that A is the region $x>0,y<x\frac{1}{\sqrt{\pi}}+1$

 

[Niles]

Hi

Thanks for that.Niles.