第2个回答 2020-06-10
令t=x+y,则y=t-x
代入圆方程:(x-2)^2+(y-1)^2=1
x^2-4x+4+t^2+x^2+1-2tx-2t+2x=1
2x^2-(2+2t)x+4+t^2-2t=0
△=(2+2t)^2-4*2*(4+t^2-2t)>=0
4t^2+4+8t-32-8t^2+16t>=0
t^2-6t+7<=0
(t-3)^2<=2
3-√2<=t<=3+√2
因为x+y>=3-√2>1
所以(x+y)^3>(x+y)^2
即∫∫(x+y)^3ds>∫∫(x+y)^2ds本回答被网友采纳