来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/08/08 03:05:55
详情见图 , 给个答案, 大哥大姐,
![](http://img.wesiedu.com/upload/1/ee/1ee92af936c5b3d0872ecb9f955519a6.jpg)
极坐标:
x = rcosθ,
y = rsinθ
极坐标下区域D: 0≤θ≤π/4 ,1≤r≤2
被积函数:y/x = tanθ ( 0≤θ≤π/4 )
arctan(y/x) = arctan(tanθ) = θ (0≤θ≤π/4)
∫∫D arctan(y/x) dσ
=∫[0,π/4] dθ ∫[1,2] rθ dr
=∫[0,π/4] θdθ ∫[1,2] r dr
= {θ|[0,π/4]}*{1/2r^2|[1,2]}
=π/4*3/2
= 3π/8