设函数f(t)连续,令F(x,y)=∫0x-y(x-y-t)f(t)dt,则( ).

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问题 设函数f(t)连续,令F(x,y)=∫0x-y(x-y-t)f(t)dt,则(          ).
   

选项 A、 
B、 
C、 
D、 

答案C

解析 因为F(x,y)=∫0x-y(x-y-t)f(t)dt=(x-y)∫0x-yf(t)dt-∫0x-ytf(t)dt,所以=∫0x-yf(t)dt+(x-y)f(x-y)-(x-y)f(x-y)=∫0x-yf(t)dt,
    =-∫0x-yf(t)dt-(x-y)f(x-y)+(x-y)f(x-y)=-∫0x-yf(t)dt,
    则
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