Question

用极坐标计算二重积分 ∫∫√(1-x^2-y^)/(1+x^2+y^2)dxdy D:x^2+y^2≤1,x≥0,y≥0

Answer 1

简单分析肆陆汪启一下，答案裂陵顷如图所示

Answer 2

极坐标下D:x^2+y^2≤1,x≥0,y≥0可表示为0≤族斗闷r≤销陪1,0≤θ≤π/2∫∫√(1-x^2-y^2)/(1+x^2+y^2)dxdy=∫兆弯(0,π/2)dθ∫(0,1)[(1-r^2)/(1+r^2)]rdr=π/2∫(0,1)[(1-r^2)/(1+r^2)]rdr,=π/2∫(0,1)r/(1+r^2)dr-(π/2)∫(0,1...