[積分] 一題重積分
Let Ω be the bounded by the y-axis,the lines y=1,y=2,and y=2x
evaluate ∫∫[1÷(x^2-y^2)]dA
如果這題使用線性轉換的話
= ∫∫[1÷(x+y)(x-y)]dA
( let u=x+y v=x-y => x=(u+v)/2 y=(u-v)/2 =>∣J∣=1/2 )
y-axis => u=-v y=2x => u=-3v
y=1 => ? y=2 => ?
該如何繼續解???
ans:-(1/2)(ln2)(ln3)
--
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 123.240.26.95
推
05/13 19:46, , 1F
05/13 19:46, 1F
推
05/14 15:59, , 2F
05/14 15:59, 2F
→
05/14 16:00, , 3F
05/14 16:00, 3F
→
05/14 16:36, , 4F
05/14 16:36, 4F
→
05/14 16:37, , 5F
05/14 16:37, 5F
討論串 (同標題文章)