问题描述: 计算二重积分:∫[0,1]dx∫[0,x^½]e^(-y²/2)dy 1个回答 分类:数学 2014-10-15 问题解答: 我来补答 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)=∫e^(-y²/2)dy-[-e^(-1/2)+∫e^(-y²/2)dy]=∫e^(-y²/2)dy+e^(-1/2)-∫e^(-y²/2)dy=e^(-1/2)=1/√e. 展开全文阅读