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

$\displaystyle \iint\limits_E \ x \mathrm{d}x\,\mathrm{d}y$

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- Mar 4th 2011, 02:09 AMmaximus101double 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

$\displaystyle \iint\limits_E \ x \mathrm{d}x\,\mathrm{d}y$ - Mar 4th 2011, 04:42 AMTKHunny
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. - Mar 5th 2011, 10:21 AMmaximus101
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