find-D-xy-1-x-2-y-2-dxdy-with-D-x-y-R-2-x-2-y-2-1-

Question Number 28448 by abdo imad last updated on 25/Jan/18

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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