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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
人气:429 ℃ 时间:2020-01-29 02:18:02
解答
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...只有D求对了 后面就太离谱了如图:
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