Question

∫∫e^z/√(x^2+y^2 ) dxdy,∑为锥面,z=√(x^2+y^2 )及平面z=1,z=2所围的立体表面的外

Answer 1

∫∫∑ e^z/√(x^2+y^2 ) dxdy ə[e^z/√(x^2+y^2 )]/əz=e^z/√(x^2+y^2 )

=∫∫∫ Ω e^z/√(x^2+y^2 ) dxdydz

=∫[0,2π]dθ ∫ [1,2] ρdρ ∫[ρ,2] e^z/ρ dz

=2π*∫[1,2](e²-e^ρ)dρ

=2πe