∫(-∞,+∞)e^[-(x^2+y^2)/2]dy=与泊松积分有关,答案是{e^[-(x^2)/2]}*√(2π),求详解

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∫(-∞,+∞)e^[-(x^2+y^2)/2]dy=与泊松积分有关,答案是{e^[-(x^2)/2]}*√(2π),求详解
∫(-∞,+∞)e^[-(x^2+y^2)/2]dy=
与泊松积分有关,答案是{e^[-(x^2)/2]}*√(2π),求详解

∫(-∞,+∞)e^[-(x^2+y^2)/2]dy=与泊松积分有关,答案是{e^[-(x^2)/2]}*√(2π),求详解

∫ <0,+∞>dx ∫ (x,√3 x)e^[-(x^2+y^2)]dy
=∫ <π/4,π/3>dt ∫ (0,+∞)e^(-r^2)rdr
=(π/12)∫ (0,+∞)(-1/2)e^(-r^2)rd(-r^2)
=(π/24)[-e^(-r^2)] (0,+∞) =π/24.