請問這題重積分如何求解?

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圖片參考：https://s.yimg.com/rk/HA05107138/o/1102945419.png


2014-11-15 21:10:50 補充：
令 I = ∫[0 to 2] ∫[y^2/4 to 1] y*arctan(x) dx dy
轉換積分次序，I = ∫[0 to 1] ∫[0 to 2√x] y*arctan(⁡x) dy dx=∫[0 to 1] 2x*arctan(⁡x) dx
=∫[0 to 1] arctan(⁡x) d(x^2) = (x^2*arctan(⁡x)|[0 to 1] - ∫[0 to 1] x^2/(1+x^2) dx
=π/4 - ∫[0 to 1] [1 - 1/(x^2+1)] dx
=π/4 - [x - arctan(⁡x)]| [0 to 1] = π/2 - 1

這里很不錯9９9ｓhｏpｐiｎg。cｏｍ老婆很喜歡
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