S为球面X2+Y2+Z2-2X-2Y-2Z+1=0,求面积分∫∫s(x+y+z)dS
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S为球面X2+Y2+Z2-2X-2Y-2Z+1=0,求面积分∫∫s(x+y+z)dS
X 2 + Y 2 + Z 2 = 2X +2 Y +2 Z
(x - 1)2 +(Y - 1)2 +(Z - 1)2 = 3
所以X = 1 + U ,Y = 1 + V,Z = 1 + W
==>Σ':U 2 + V 2 + W 2 = 3
I =∫∫Σ(X 2 + Y 2)德尚 BR /> =∫∫Σ'[(1 + U)2 +(1 + V)2]副
=∫∫Σ'(U 2 + V 2 + 2 + 2U + 2V)德尚
> = 2∫∫Σ'U 2 DS + 2∫∫Σ'德尚
=(2/3)∫∫Σ'(U 2 + V 2 + W 2)DS + 2∫∫Σ'德尚 =(2/3)∫∫Σ'(3)DS + 2∫∫Σ'德尚
= [(2/3)(3)+ 2]∫∫Σ'德尚
= 4 *(4π)(3)
=48π
(x - 1)2 +(Y - 1)2 +(Z - 1)2 = 3
所以X = 1 + U ,Y = 1 + V,Z = 1 + W
==>Σ':U 2 + V 2 + W 2 = 3
I =∫∫Σ(X 2 + Y 2)德尚 BR /> =∫∫Σ'[(1 + U)2 +(1 + V)2]副
=∫∫Σ'(U 2 + V 2 + 2 + 2U + 2V)德尚
> = 2∫∫Σ'U 2 DS + 2∫∫Σ'德尚
=(2/3)∫∫Σ'(U 2 + V 2 + W 2)DS + 2∫∫Σ'德尚 =(2/3)∫∫Σ'(3)DS + 2∫∫Σ'德尚
= [(2/3)(3)+ 2]∫∫Σ'德尚
= 4 *(4π)(3)
=48π
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