已知∫(0,+∞)e^[-(x^2)]dx=√π/2,证明∫(-∞,+∞)x^2e^[-(x^2)]dx=√π/2,求详解._数学解答 - 作业小助手

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已知∫(0,+∞)e^[-(x^2)]dx=√π/2,证明∫(-∞,+∞)x^2e^[-(x^2)]dx=√π/2,求详解.

人气：434 ℃　时间：2020-06-19 21:06:26

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

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