计算三重积分fffxdxdydz平面x+y+z-2iik
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发布时间：2022-10-28 11:22
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热心网友
时间：2023-10-06 07:40
∫∫∫Ω x dxdydz
= ∫(0,2) x dx ∫(0,2 - x) dy ∫(0,2 - x - y) dz
= ∫(0,2) x dx ∫(0,2 - x) (2 - x - y) dy
= ∫(0,2) x (2y - xy - y²/2)：(0,2 - x) dx
= ∫(0,2) x [ 2 (2 - x) - x (2 - x) - (1/2) (2 - x)² ] dx
= ∫(0,2) x [ (4 - 2x) - (2x - x²) - (2 - 2x + x²/2) ] dx
= ∫(0,2) x (x²/2 - 2x + 2) dx
= ∫(0,2) (x³/2 - 2x² + 2x) dx
= (1/2 * x⁴/4 - 2 * x³/3 + x²)：(0,2)
= 1/2 * 1/4 * 16 - 2/3 * 8 + 4
= 2/3
