计算x2dydz+y2dzdx+z2dxdy,其中∑:(x-1)2+(y一1)2+=1(y≥1),取外侧.

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问题 计算x2dydz+y2dzdx+z2dxdy,其中∑:(x-1)2+(y一1)2=1(y≥1),取外侧.

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答案令∑0:y=1(Dxz:(x一1)2+[*]≤1),取左侧, 则原式=[*]x2dydz+y2dzdx+z2dxdy-[*]x2dydz+y2dzdx+z2dxdy=I1-I2, [*]

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