• 2022-06-09 问题

    计算\(\int\!\!\!\int\limits_\sum { { x^2}dydz + {y^2}dzdx + {z^2}} dxdy\),其中\(\sum\)为长方体\(\Omega \)的整个表面外侧,\(\Omega = \{ (x,y,z)|0 \le x \le a,0 \le y \le b,0 \le z \le c\} \)。 A: \((a + b + c)abc\) B: \((a -b + c)abc\) C: \((a + b -c)abc\) D: \((a - b - c)abc\)

    计算\(\int\!\!\!\int\limits_\sum { { x^2}dydz + {y^2}dzdx + {z^2}} dxdy\),其中\(\sum\)为长方体\(\Omega \)的整个表面外侧,\(\Omega = \{ (x,y,z)|0 \le x \le a,0 \le y \le b,0 \le z \le c\} \)。 A: \((a + b + c)abc\) B: \((a -b + c)abc\) C: \((a + b -c)abc\) D: \((a - b - c)abc\)

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