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Question Number 78706 by abdomathmax last updated on 20/Jan/20
calculate ∫∫_([0,1]^2 ) ((dxdy)/((x+y+1)^2 ))
calculate∫∫[0,1]2dxdy(x+y+1)2
Answered by mind is power last updated on 20/Jan/20
=∫_0 ^1 −[(1/(x+y+1))]_0 ^1 dx =∫_0 ^1 −(1/(x+2))−(1/(x+1))dx =−ln(3)+ln(2)−ln(2)=ln((1/3))
=∫01−[1x+y+1]01dx=∫01−1x+2−1x+1dx=−ln(3)+ln(2)−ln(2)=ln(13)

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