计算二重积分∫∫D根号(x^2+y^2)dσ,其中D 是x^2+y^2=2x 所围成的区域,

2024-11-07 18:07:59
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回答1:

∫∫D根号(x^2+y^2)dσ=2∫(0,π/2)dθ∫(0,2cosθ)r^2dr
=2∫(0,π/2)(1/3)(2cosθ)^3dθ=(16/3)∫(0,π/2)(cosθ)^3dθ=(16/3)(2/3)=32/9