find ∫∫_D ((xy)/(1+x^2 +y^2 ))dxdy with D= {(x,y)∈R^2 / x^2 +y^2 ≥1 } .


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Question Number 28448 by abdo imad last updated on 25/Jan/18
$find ∫∫_D ((xy)/(1+x^2 +y^2 ))dxdy with D= {(x,y)∈R^2 / x^2 +y^2 ≥1 } .$
$f i n d \int \int_{D} \frac{x y}{1 + x^{2} + y^{2}} d x d y w i t h$ $D = {(x, y) \in R^{2} / x^{2} + y^{2} ⩾ 1} .$
	Answered by ajfour last updated on 26/Jan/18

	$l e t x = r \cos θ, y = r \sin θ$ $\int_{1}^{\infty} \int_{0}^{2 π} \frac{r^{2} \sin θ \cos θ}{1 + r^{2}} (r d θ d r)$ $= 0 .$
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