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find double integral of x times y time e to the <x plus y> . bounded from <0,1> x <0,1>

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∫xe^xdx
= (x-1)e^x
Evaluation from 0 to 1 gives [0-(-1)]=1

Since x and y are two independent variables,
∫∫xye^x+ydxdy
∫∫xe^x ye^ydxdy
=∫xe^xdx ∫ye^ydy
=1*1
=1

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