Question

高数问题求解答过程

Answer 1

质量M=∫∫ρdS
=∫∫1/z dS
=∫∫1/√(a²-x²+y²）a/√(a²-x²+y²）dxdy
=∫∫adxdy
=a∫∫dxdy
=πa^3
注：1、z=√(a²-x²+y²）代入
2、dS=√1+Zx²+Zy²dxdy

追问

答案是paialn2

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追答

质量M=∫∫ρdS
=∫∫1/z dS
=∫∫1/√(a²-x²+y²）a/√(a²-x²+y²）dxdy
=∫∫a/(a²-x²+y²）dxdy
=a∫∫1/(a²-ρ²)xρdθρdρ
=a∫dθ∫1/(a²-ρ²)xρdρ（θ的下限为0,上限为2π;ρ的下限为0,上限为a)
=πaln2
注：1、z=√(a²-x²+y²）代入
2、dS=√1+Zx²+Zy²dxdy