估算范围：I=∫∫xy(x+y)dσ,其中D={（x,y）/0≦x≦1,0≦y≦2}.

Question

估算范围：I=∫∫xy(x+y)dσ,其中D={（x,y）/0≦x≦1,0≦y≦2}.

Answer 1

当0≦x≦1,0≦y≦2时,0≦xy(x+y)≦1*2*(1+2)=6.而积分区域（矩形）面积为1*2=2,所以
0*2≦∫∫xy(x+y)dσ0≦6*2,即0≦∫∫xy(x+y)dσ≦12