设D由y=及x轴围成,f(x,y)=xy—f(x,y)dxdy,求f(x,y)=________.

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问题 设D由y=及x轴围成,f(x,y)=xy—f(x,y)dxdy,求f(x,y)=________.

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答案f(x,y)=xy-[*]

解析 令A=f(x,y)dxdy,则f(x,y)=xy—A,积分得
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