作者airslas2012 (天蔚藍)
看板Math
標題[微積] (cscx)^2積分？
時間Thu Apr 14 23:25:32 2011
http://tinyurl.com/3jovf3j
請問這樣算有錯嗎？
感覺有點怪怪的，最後X是併到C裡面？
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1F：推 ss1132 :sinx=u 那麼cosx跟u就有關係啦 04/14 23:27
2F：→ airslas2012 :果然..... 04/14 23:28
3F：→ mk426375 :第四個等號出問題 04/14 23:28
4F：→ airslas2012 :不過我是令成(dsinx)...只對dsinx去積分 04/14 23:28
5F：→ airslas2012 :這樣還有關？ 04/14 23:29
6F：推 ss1132 :對 04/14 23:29
7F：→ airslas2012 :okay 那 cos^2/sin^2 有什麼積分方法比較好? 04/14 23:30
8F：推 ss1132 :還記得cotx的微分嗎? 04/14 23:33
9F：→ ss1132 :可以直接用... 04/14 23:33
10F：→ airslas2012 :ln sin 我用用看 感謝~ 04/14 23:33
11F：→ airslas2012 :囧技成積分的去了 04/14 23:35
12F：→ airslas2012 :cotx的微分我會阿，我想把csc^2推回去cotx ~ 04/14 23:35
14F：→ airslas2012 :這樣應該沒錯了吧?! 04/14 23:55
15F：推 ss1132 :可以在c/(s^2) ds的時候就用分部積分 04/15 00:15
16F：推 math1209 :Let t = csc x + cot x, then we have 04/15 00:49
17F：→ math1209 :(1) dt/t = csc x dx. (2) (t + 1/t)/2 = csc x. 04/15 00:50
18F：→ math1209 :Using above, we can calculate S (csc x)^n dx for 04/15 00:51
19F：→ math1209 :any positive integer n, and similarly for secx. 04/15 00:51
20F：→ math1209 :(1) is wrong, and (1) should be dt/t = - csc x dx 04/15 00:52
21F：→ math1209 :For example, S (csc x)^2 dx = S csc x (csc x) dx 04/15 00:54
22F：→ math1209 : = -1/2 S 1 + t^(-2) dt = ... . 04/15 00:54
23F：→ airslas2012 :BUT there's some problem 04/15 01:10
24F：→ airslas2012 :last i get -1/2[t-1/t]+c 04/15 01:10
25F：→ airslas2012 :BUT t+1/t seems equal to zero ? 04/15 01:11
26F：→ airslas2012 :================================================= 04/15 01:12
27F：→ airslas2012 :(csc+cot)-1/(csc+cot) = (csc^2-cot^2-1)/(csc+cot) 04/15 01:13
28F：→ airslas2012 :and we know 1+cot^2=csc^2 so csc^2-cot^2-1 = 0 04/15 01:14
29F：→ airslas2012 :SORRY MY FAULT ~ 04/15 01:16
30F：→ airslas2012 :I GET IT THANK YOU VERY MUCH 04/15 01:17