计算二重积分

来源：百度知道 编辑：UC知道 时间：2024/04/29 14:31:32
∫∫∣sin (x+y) ∣dxdy,其中D为矩形区域0<=x<=π,0<=y<=π.
D

D区域分为:
D1: 0<=x<=π/2, 0<=y<=π/2-x.
D2: 0<=y<=π/2, π/2-y<=x<=π
D3: π/2<=y<=π, 0<=x<=3π/2-y
D4: π/2<=x<=π, 3π/2-x<=y<=π
化成2次积分做就可以了.
∣sin (x+y) ∣ 在 D1,D4 中为正, 在 D2,D3中为负.
D1 由 0<=x+y<=π/2 而来.
D2,D3 由π/2<=x+y<=3π/2 而来.
D4 由 3π/2<=x+y<=2π 而来.