Upgrade to access all content for this subject

Evaluate the following integrals by using appropriate symmetry arguments:

$$I=\iint_R 2xye^{-x^2-y^2}dA$$

...where $R$ is a plane region given by:

$$R=\{(x,y): -1\leq x\leq 1, -2\leq y\leq 2\}$$

$-2$

$-1$

$0$

$1$

$2$