∫(-∞,+∞)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
网友回答
∫(-∞,+∞)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(图1)
======以下答案可供参考======
供参考答案1:
∫ dx ∫ (x,√3 x)e^[-(x^2+y^2)]dy
=∫ 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.