计算二次积分:∫(1,3)dx∫(2,x-1)sin(y^2)dy

积分区域 D:x-1 ≤ y ≤ 2,1≤ x ≤3
视为Y型区域,即：1 ≤ x ≤ y+1,0 ≤ y ≤ 2
I = ∫[0,2] sin(y²)dy ∫[1,y+1] dx 交换积分次序
= ∫[0,2] y sin(y²) dy = (-1/2) cos(y²) |[0,2]
= 1/2﹣(1/2)cos4