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calculate-D-x-2-y-2-xy-dxdy-with-D-x-y-R-2-0-y-1-and-2-x-5-




Question Number 59162 by maxmathsup by imad last updated on 05/May/19
calculate  ∫∫_D   (√(x^2 −y^2 ))xy dxdy  with  D ={(x,y)∈ R^2    /0≤y≤1  and  2 ≤x ≤5 }
$${calculate}\:\:\int\int_{{D}} \:\:\sqrt{{x}^{\mathrm{2}} −{y}^{\mathrm{2}} }{xy}\:{dxdy}\:\:{with} \\ $$$${D}\:=\left\{\left({x},{y}\right)\in\:{R}^{\mathrm{2}} \:\:\:/\mathrm{0}\leqslant{y}\leqslant\mathrm{1}\:\:{and}\:\:\mathrm{2}\:\leqslant{x}\:\leqslant\mathrm{5}\:\right\} \\ $$

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