单选题 难度 3

二次积分 I=∫02dx∫0x2/2f(x,y) dy+∫222dx∫08−x2f(x,y) dyI=\int_0^2 dx\int_0^{x^2/2} f(x,y)\,dy+\int_2^{2\sqrt2} dx\int_0^{\sqrt{8-x^2}} f(x,y)\,dy 交换积分次序后化为( )

  1. 选项 A ∫02dy∫222f(x,y) dx\int_0^2 dy\int_2^{2\sqrt2} f(x,y)\,dx
  2. 选项 B ∫02dy∫x2/28−x2f(x,y) dx\int_0^2 dy\int_{x^2/2}^{\sqrt{8-x^2}} f(x,y)\,dx
  3. 选项 C ∫022dy∫x2/28−y2f(x,y) dx\int_0^{2\sqrt2} dy\int_{x^2/2}^{\sqrt{8-y^2}} f(x,y)\,dx
  4. 选项 D ∫02dy∫2y8−y2f(x,y) dx\int_0^2 dy\int_{\sqrt{2y}}^{\sqrt{8-y^2}} f(x,y)\,dx

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