计算二重积分：∫[0,1]dx∫[0,x^½]e^(-y²/2)dy
计算二重积分：∫[0,1]dx∫[0,x^½]e^(-y²/2)dy
数学人气：812 ℃时间：2020-04-05 05:38:08
优质解答
原式=∫dy∫e^(-y²/2)dx (作积分顺序变换)=∫(1-y²)e^(-y²/2)dy=∫e^(-y²/2)dy-∫y²e^(-y²/2)dy=∫e^(-y²/2)dy-{[-ye^(-y²/2)]│+∫e^(-y²/2)dy} (应用分部积分法)=∫...
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