高数对弧长的曲线积分问题
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发布时间:2022-12-21 04:47
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时间:2023-10-05 05:17
∫【L】x²yzds
=∫【AB】x²yzds+∫【BC】x²yzds+∫【CD】x²yzds
而 ∫【AB】x²yzds (AB上 : x=0, y=0, z=t, 0<=t<=2 ) = ∫【0,2】0²0*2dt= 0
∫【BC】x²yzds (BC上 : x=t, 0<=t<=1, y=0, z=2) = ∫【0,1】t²0*2dt= 0
∫【CD】x²yzds (CD上 : x=1, y=t , 0<=t<=3, z=2 ) = ∫【0,3】1²t*2dt= 9
故 原式 = 9。