设f(x,y)连续,且f(x,y)=xy+f(x,y)dσ,其中D由y=0,y=x2及x=1围成,则f(x,y)=_______.

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问题 设f(x,y)连续,且f(x,y)=xy+f(x,y)dσ,其中D由y=0,y=x2及x=1围成,则f(x,y)=_______.

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答案[*]

解析f(x,y)dσ=k,则f(x,y)=xy+k,两边在D上积分得
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