Asked by christine
please help emergency.
find double integral of x times y time e to the <x plus y> . bounded from <0,1> x <0,1>
find double integral of x times y time e to the <x plus y> . bounded from <0,1> x <0,1>
Answers
Answered by
MathMate
∫xe<sup>x</sup>dx
= (x-1)e<sup>x</sup>
Evaluation from 0 to 1 gives [0-(-1)]=1
Since x and y are two independent variables,
∫∫xye<sup>x+y</sup>dxdy
∫∫xe<sup>x</sup> ye<sup>y</sup>dxdy
=∫xe<sup>x</sup>dx ∫ye<sup>y</sup>dy
=1*1
=1
= (x-1)e<sup>x</sup>
Evaluation from 0 to 1 gives [0-(-1)]=1
Since x and y are two independent variables,
∫∫xye<sup>x+y</sup>dxdy
∫∫xe<sup>x</sup> ye<sup>y</sup>dxdy
=∫xe<sup>x</sup>dx ∫ye<sup>y</sup>dy
=1*1
=1
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