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find-the-value-of-I-D-x-3-dxdy-with-D-x-y-R-2-1-x-2-and-x-2-y-2-1-




Question Number 28685 by abdo imad last updated on 28/Jan/18
find the value of  I=∫∫_D  x^3 dxdy   with  D= {(x,y)∈R^2 /1≤x≤2 and  x^2 −y^2   ≥1  }.
$${find}\:{the}\:{value}\:{of}\:\:{I}=\int\int_{{D}} \:{x}^{\mathrm{3}} {dxdy}\:\:\:{with} \\ $$$${D}=\:\left\{\left({x},{y}\right)\in{R}^{\mathrm{2}} /\mathrm{1}\leqslant{x}\leqslant\mathrm{2}\:{and}\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:\:\geqslant\mathrm{1}\:\:\right\}. \\ $$

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