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find-A-x-y-e-x-e-y-dxdy-with-A-x-y-R-2-x-0-y-0-x-y-1-




Question Number 28446 by abdo imad last updated on 25/Jan/18
find ∫∫_A (x+y) e^(−x)  e^(−y)  dxdy with  A= {(x,y)∈R^2   /x≥0 ,y≥0 , x+y ≤1 }  .
$${find}\:\int\int_{{A}} \left({x}+{y}\right)\:{e}^{−{x}} \:{e}^{−{y}} \:{dxdy}\:{with} \\ $$$${A}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} \:\:/{x}\geqslant\mathrm{0}\:,{y}\geqslant\mathrm{0}\:,\:{x}+{y}\:\leqslant\mathrm{1}\:\right\}\:\:. \\ $$

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