设区域D={(x,y)|0≤x≤1,0≤y≤1},则|y-x2|dxdy=_______.

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问题 设区域D={(x,y)|0≤x≤1,0≤y≤1},则|y-x2|dxdy=_______.

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答案[*]

解析 令D1=((x,y)|0≤x≤1,0≤y≤x2},D2={(x,y)|0≤x≤1,x2≤y≤1},

|y-x2|dxdy=∫01dx∫0x2(x2-y)dy+∫01dx∫x21(y-x2)dy
=∫01=∫01)x4-x2+
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