二重积分的极坐标.此题不懂,
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二重积分的极坐标.
![](http://img.wesiedu.com/upload/b/66/b66a0f4f43c5cf4fbb4b62b3bb7e3d89.jpg)
此题不懂,
![](http://img.wesiedu.com/upload/b/66/b66a0f4f43c5cf4fbb4b62b3bb7e3d89.jpg)
此题不懂,
![二重积分的极坐标.此题不懂,](/uploads/image/z/18378647-71-7.jpg?t=%E4%BA%8C%E9%87%8D%E7%A7%AF%E5%88%86%E7%9A%84%E6%9E%81%E5%9D%90%E6%A0%87.%E6%AD%A4%E9%A2%98%E4%B8%8D%E6%87%82%2C)
∫∫ln(1+x^2+y^2)dxdy
=∫∫ln(1+ρ^2)ρdρdθ
=(1/2)∫dθ∫ln(1+ρ^2)d(1+ρ^2)
=(1/2)∫dθ[(1+ρ^2)ln(1+ρ^2)-(1+ρ^2)] (ρ从0到1)
=(1/2)∫dθ*(2ln2-1) (θ从0到π/2)
=(2ln2-1)π/4
=∫∫ln(1+ρ^2)ρdρdθ
=(1/2)∫dθ∫ln(1+ρ^2)d(1+ρ^2)
=(1/2)∫dθ[(1+ρ^2)ln(1+ρ^2)-(1+ρ^2)] (ρ从0到1)
=(1/2)∫dθ*(2ln2-1) (θ从0到π/2)
=(2ln2-1)π/4