企源知识库

计算二重积分∫∫_D[y/(1+x²)]dσ，其中D是区域：0≤x≤1;-1≤y≤0．
【正确答案】：∫∫_D[y/(1+x²)]dσ=∫₀¹dx∫_-1⁰[y/(1+x²)]dy =∫₀¹[1/(1+x²)]•[(1/2)y²∣_-1⁰]dx =-(1/2)∫₀¹[1/(1+x²)]dx=-(1/2)•arctanx∣₀¹ =-(π/8)