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极坐标下D:x^2+y^2≤1，x≥0，y≥0可表示为0≤r≤1,0≤θ≤π/2∫∫√(1-x^2-y^2)/(1+x^2+y^2)dxdy=∫(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)r^3/(1+r^2)dr,=π/2∫(0,1)r/(1+r^2)dr-(π/2)∫(0,1)[(r^3+r)-r]/(1+r^2)dr=2*(π/2)∫(0,1)r/(1+r^2)dr-(π/2)∫(0,1)rdr=(π/2)ln(1+r^2)|(0,1)-(π/2)*(1/2)r^ |
