Multivariable Calculus

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Moderate

Integration Using Symmetry

MVCALC-PPJTLY

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:

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

A

$-2$

B

$-1$

C

$0$

D

$1$

E

$2$