calculate-x-2-y-2-1-dxdy-3-x-2-y-2-

Question Number 28158 by abdo imad last updated on 21/Jan/18

c a l c u l a t e \int \int_{x^{2} + y^{2} ⩽ 1} \frac{d x d y}{3 + x^{2} + y^{2}} .

Answered by ajfour last updated on 21/Jan/18

x^{2} + y^{2} = r^{2}

d x d y = r d r d θ

\Rightarrow I = \int_{0}^{2 π} [\int_{0}^{1} (\frac{r d r}{3 + r^{2}}) d θ

= π \ln (\frac{4}{3}) .

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