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Question Number 36948 by maxmathsup by imad last updated on 07/Jun/18

calculate   ∫∫_D (√(xy)) dxdy  with  D={(x,y)∈R^2  / (x+y)^2  ≥2x  and xy≥0}

$${calculate}\:\:\:\int\int_{{D}} \sqrt{{xy}}\:{dxdy}\:\:{with} \\ $$$${D}=\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} \:/\:\left({x}+{y}\right)^{\mathrm{2}} \:\geqslant\mathrm{2}{x}\:\:{and}\:{xy}\geqslant\mathrm{0}\right\} \\ $$

Commented by ajfour last updated on 07/Jun/18

shouldn′t it be    (x+y)^2  ≤ 2x    ?

$${shouldn}'{t}\:{it}\:{be} \\ $$$$\:\:\left({x}+{y}\right)^{\mathrm{2}} \:\leqslant\:\mathrm{2}{x}\:\:\:\:? \\ $$

Commented by prof Abdo imad last updated on 07/Jun/18

no sir Ajfour ...

$${no}\:{sir}\:{Ajfour}\:... \\ $$

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