高数曲线积分和曲面积分

2024-11-20 06:27:54
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回答(1):

7/10. 用高斯公式得 I = ∫∫∫<Ω>3dv = 4πa^3.
6/10. 用高斯公式得
I = ∫∫∫<Ω>(y+x)dv = ∫<0, a>dz∫<0, a>dy∫<0, a>(x+y)dx
= ∫<0, a>dz∫<0, a>dy[x^2/2 + yx]<0, a>
= ∫<0, a>dz∫<0, a>(a^2/2 + ay)dy
= a[a^2y/2 + ay^2/2]<0, a> = a^4