计算二重积分∫∫|y-x^2|dxdy,其中区域D={(x,y)|0<=x<=1,0<=y<=1}

2024-11-09 02:57:38
推荐回答(2个)
回答1:

区域D={(x,y)|0<=x<=1,0<=y<=1}分为2部分:
D1={(x,y)|0<=x<=1,0<=y<=x²}
D2={(x,y)|0<=x<=1,x²<=y<=1}
∫∫[D] |y-x²| dxdy
=∫∫【0<=x<=1,0<=y<=x²】(-y+x²)dxdy+∫∫【0<=x<=1,x²<=y<=1】(y-x²)dxdy
=∫【0,1】dx∫【0,x²】(-y+x²)dy+∫【0,1】dx ∫【x²,1】(y-x²)dy
=1/2

回答2:

简单分析一下,答案如图所示