∫(-∞,+∞)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

来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/27 17:47:37
∫(-∞,+∞)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+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.