Re: [問題] an integral question

看板NTUCHE-02-HW作者 (摩卡金幣)時間14年前 (2009/11/14 01:26), 編輯推噓1(1推 0噓 6→)
留言7則, 3人參與, 最新討論串2/2 (看更多)
※ 引述《i563214f (i563214f)》之銘言： ∫ ln(sin(x))dx x from 0 to π/2 please tell me how to calculate this question thank you Let I=∫ln(sinx)dx x from 0 to pi/2 ---1 PROPERTY:∫f(x)dx x from 0 to a =∫f(a-x)dx x from 0 to a I=∫ln(sin(pi/2-x))dx=∫ln(cosx)dx ---2 1+2:2I=∫(lnsinx+lncosx)dx =∫ln(sinxcosx)dx =∫ln(sin2x/2)dx =∫(ln(sin2x)-ln2)dx =∫(ln(sin2x)dx-∫(ln2)dx =∫(ln(sin2x)dx-ln2*x|x from 0 to pi/2 =1/2∫ln(sinu)du-ln2*pi/2 u from 0 to pi =1/2*2∫ln(sinu)du-ln2*pi/2 (PROPERTY) =∫ln(sinu)du-ln2*pi/2 =I-ln2*pi/2 2I=I-ln2*pi/2 I=ln2*(-pi/2) 以上= = -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.242.92
推
11/14 00:38,
同學你題目有打錯嗎? 我畫圖+計算機+網頁積分器
11/14 00:38
→
11/14 00:38,
三種方法算出來都是無解
11/14 00:38
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11/14 00:45,
算不出+1
11/14 00:45
推
11/14 00:57,
這題不能解阿
11/14 00:57
-- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 140.112.211.173
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11/14 01:28, , 1F
倒數第六行的x from 0 to pi/2
11/14 01:28, 1F
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11/14 02:12, , 2F
ln(x) x不能等於0 這篇是....
11/14 02:12, 2F
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11/14 02:15, , 3F
x沒有等於0啊!只是從0積到pi/2
11/14 02:15, 3F
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11/14 02:22, , 4F
從0積到pi/2不用等於0= =?
11/14 02:22, 4F
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11/14 02:23, , 5F
他根本不會形成封閉的區塊...哪來的面積
11/14 02:23, 5F
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11/14 02:34, , 6F
好ㄅ~我錯了
11/14 02:34, 6F
推
11/14 02:40, , 7F
這是有名難題~如果有人能不看解答解出來~真的超強!!
11/14 02:40, 7F
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文章代碼(AID): #1A_PR2nJ (NTUCHE-02-HW)
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文章代碼(AID): #1A_PR2nJ (NTUCHE-02-HW)