# Thread: double integral for a given region E

1. ## double integral for a given region E

Let $\displaystyle E \subset \Re ^2$ be the region
{$\displaystyle (x, y) | y \le |x| , x^2 + y^2 \le 4$}
Evaluate
$\displaystyle \iint\limits_E \ y \mathrm{d}x\,\mathrm{d}y$
and
$\displaystyle \iint\limits_E \ x \mathrm{d}x\,\mathrm{d}y$

2. Two things:

1) Must we use dxdy or will dydx do for some pieces?
2) The second is obviously zero (0) - by symmetry. No need to play with that one.

3. Originally Posted by TKHunny
Two things:

1) Must we use dxdy or will dydx do for some pieces?
2) The second is obviously zero (0) - by symmetry. No need to play with that one.
Hi, I'm a bit confused,

I do not know how to solve these types of integrals, is it like integrating the one on the inside with limits, then the one on the outside is applied to the
answer with the new limits, and I'm not sure how to obtain these limits, I can possibly draw this region but were do I go from there?

with 1)
I think it has something to do with changing the order of integration

2) we get zero by symmetry as the answer?

thank you