[積分] 反三角積分

看板trans_math作者 (Ryan)時間13年前 (2012/07/01 00:52), 編輯推噓2(2推 0噓 32→)
留言34則, 3人參與, 最新討論串1/1
1 ∫x*arctan(x^2) dx =_____. 0 -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 111.249.229.110
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07/01 01:00, , 1F
...... u=x^2 ~
07/01 01:00, 1F
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07/01 01:06, , 2F
我是最後卡住...
07/01 01:06, 2F
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07/01 01:09, , 3F
(1/2)∫arctan(u) du = ...
07/01 01:09, 3F
推
07/01 01:15, , 4F
h=arctanu,dk=du
07/01 01:15, 4F
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07/01 01:18, , 5F
dk=du ?!
07/01 01:18, 5F
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07/01 01:21, , 6F
dh=1/(1+x^2),k=u..像uv-∫vdu
07/01 01:21, 6F
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07/01 01:27, , 7F
不過用分部積分，似乎沒辦法消掉arctan
07/01 01:27, 7F
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07/01 01:28, , 8F
hk-∫kdh = arctan(u)/1+x^2-∫kdh
07/01 01:28, 8F
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07/01 01:31, , 9F
=>uarctanu-∫u/(1+u^2)du..應該吧QQ
07/01 01:31, 9F
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07/01 01:32, , 10F
更正:hk-∫kdh = u*arctan(u)-∫kdh
07/01 01:32, 10F
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07/01 01:34, , 11F
阿...你算算看囉~ 真的算得出來嗎?! = =
07/01 01:34, 11F
推
07/01 01:35, , 12F
∫kdh那邊就可以積了吧,我還沒帶0,1進
07/01 01:35, 12F
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07/01 01:35, , 13F
去的說
07/01 01:35, 13F
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07/01 01:38, , 14F
嗯嗯 好像可以耶~
07/01 01:38, 14F
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07/01 01:43, , 15F
答案是:(pi/4)-(ln2/2)嗎?!
07/01 01:43, 15F
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07/01 01:49, , 16F
我比你多一個1/2,會不會剛開始那邊
07/01 01:49, 16F
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07/01 01:52, , 17F
成大100解答哪裡有阿?!
07/01 01:52, 17F
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07/01 01:54, , 18F
原來是成大100=.=自己做過自己都忘記
07/01 01:54, 18F
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07/01 01:55, , 19F
所以是(1/2)[pi/4)-(ln2/2)]這樣囉~
07/01 01:55, 19F
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07/01 01:55, , 20F
答案是 pi/8 - (ln2)/4
07/01 01:55, 20F
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07/01 01:56, , 21F
嗯嗯對
07/01 01:56, 21F
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07/01 01:57, , 22F
晚上算微積分算到快趴了...@@
07/01 01:57, 22F
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07/01 01:58, , 23F
可以提供成大100嗎?! 0..0
07/01 01:58, 23F
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07/01 01:58, , 24F
真的!!!血糖太低T^T
07/01 01:58, 24F
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07/01 01:59, , 25F
你要哪幾題..
07/01 01:59, 25F
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07/01 02:00, , 26F
冏了...這題不難...卻卡了這麼久...@@
07/01 02:00, 26F
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07/01 02:01, , 27F
我也常降..超囧
07/01 02:01, 27F
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07/01 02:01, , 28F
可以的話都給吧~考試逼近....急需~
07/01 02:01, 28F
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07/01 02:02, , 29F
轉板上互相幫忙...感覺真得很溫馨...
07/01 02:02, 29F
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07/01 02:05, , 30F
1a:DNE1b:e^-1/2.3a:2ln(ln4)-2ln(ln2)
07/01 02:05, 30F
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07/01 02:08, , 31F
6:1/(2pi)。7:ln|y/x|
07/01 02:08, 31F
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07/01 02:10, , 32F
8:dmin=5^(1/2)發生在(x,y)=(+-1,+-2)
07/01 02:10, 32F
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07/01 02:13, , 33F
4:[243/28+3/2-1/12-1/252-1/18+1/4]pi
07/01 02:13, 33F
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07/01 03:01, , 34F
謝謝哟~ 一起甲幼吧!!
07/01 03:01, 34F
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