计算∫(0,1)dx∫(x,1)e^(y^2)dy=

题目

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

答案

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)