已知∫(0,+∞)e^[-(x^2)]dx=√π/2,证明∫(-∞,+∞)x^2e^[-(x^2)]dx=√π/2,求详解.
问题描述：
已知∫(0,+∞)e^[-(x^2)]dx=√π/2,证明∫(-∞,+∞)x^2e^[-(x^2)]dx=√π/2,求详解.
答
你题目写错了,应该是证明∫(0,+∞)x^2e^[-(x^2)]dx=√π/2.
证明见图片,用换元积分法