设区域D由x=0,y=0,x+y=,x+y=1围成,若I1=[ln(x+y)]3dxdy,I2=(x+y)3dxdy,I3=sin3(x+y)dxdy,则( )

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问题 设区域D由x=0,y=0,x+y=,x+y=1围成,若I1=[ln(x+y)]3dxdy,I2=(x+y)3dxdy,I3=sin3(x+y)dxdy,则(    )

选项 A、I1>I2>I3
B、I2>I3>I1
C、I1<I2<I3
D、I2<I3<I1

答案B

解析≤x+y≤1得[ln(x+y)]3≤0,于是I1=[ln(x+y)]3dxdy≤0;
≤x+y≤1时,由(x+y)3≥sin3(x+y)≥0得I2≥I3≥0,
故I2≥I3≥I1,应选(B)
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