计算[0,π/2]∫dΘ[0-cosΘ]∫rdr

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计算[0,π/2]∫dΘ[0-cosΘ]∫rdr计算[0,π/2]∫dΘ[0-cosΘ]∫rdr计算[0,π/2]∫dΘ[0-cosΘ]∫rdr∫[0,π/2]dΘ∫[0-cosΘ]rdr=∫[0,π

计算[0,π/2]∫dΘ[0-cosΘ]∫rdr
计算[0,π/2]∫dΘ[0-cosΘ]∫rdr

计算[0,π/2]∫dΘ[0-cosΘ]∫rdr
∫[0,π/2]dΘ∫[0-cosΘ]rdr
=∫[0,π/2]1/2r² |[0-cosΘ] dΘ
=1/2∫[0,π/2]cos²Θ] dΘ
=1/4∫[0,π/2](1+cos2Θ) dΘ
=1/4(Θ+1/2sin2Θ) |[0,π/2]
=π/8