设平面D由x+y=,x+y =1及两条坐标轴围成,I1=ln(x+y)3dxdy,I2=(x+y)3dxdy,I3=sin(x+y)I3dxdy,则( )

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问题 设平面D由x+y=,x+y =1及两条坐标轴围成,I1=ln(x+y)3dxdy,I2=(x+y)3dxdy,I3=sin(x+y)I3dxdy,则(     )

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

答案C

解析 显然在D上0<x+y≤1,则ln(x+y)3≤0,0<sin(x+y)3<(x+y)3,从而有ln(x+y)3dxdy<sin(x+y)3dxdy<(x+y)3dxdy,故选C。
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