Re: [積分] special的重積分

[Honor1984 (希望願望成真)]

※ 引述《midarmyman (midarmyman)》之銘言：
:            1
: ∫∫--------------dxdy
:      √(xy(1-x-y))
: 範圍是x=0 y=0  x+y=1

u = x + y

v = x - y

            1
 ∫∫--------------dxdy
      √(xy(1-x-y))

   1  -u     2  Jacobian
= ∫∫------------------------dvdu
   0  u √[(u^2 - v^2)(1 - u)]

= 2π

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推 Frobenius:推～
推 retryi12:新招~
推 midarmyman:謝了
推 midarmyman:現在發現這應該才是正規的
→ midarmyman:這題放的章節就是坐標變換 XD
推 midarmyman:v的上下限是不是反了?
→ midarmyman:沒事 是我看反了= =