计算∫(0,1)dx∫(x,1)e^(y^2)dy=

学习时间:2026-10-09 16:56:57 阅读：7995

计算∫(0,1)dx∫(x,1)e^(y^2)dy= 答案是1/2(1-1/e),求详细解答

怡然的老师

2026-10-09 16:56:57

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题目应该是e^(-y^2)交换积分次序：= ∫(0,1)dy ∫(0,y) e^(-y^2) dx= ∫(0,1) ye^(-y^2)dy= 1/2 * ∫(0,1) e^(-y^2)dy^2= 1/2 * (1-1/e)