作者airslas2012 (天蔚蓝)
看板Math
标题[微积] (cscx)^2积分？
时间Thu Apr 14 23:25:32 2011
http://tinyurl.com/3jovf3j
请问这样算有错吗？
感觉有点怪怪的，最後X是并到C里面？
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※ 发信站: 批踢踢实业坊(ptt.cc)
◆ From: 118.171.225.45
1F：推 ss1132 :sinx=u 那麽cosx跟u就有关系啦 04/14 23:27
2F：→ airslas2012 :果然..... 04/14 23:28
3F：→ mk426375 :第四个等号出问题 04/14 23:28
4F：→ airslas2012 :不过我是令成(dsinx)...只对dsinx去积分 04/14 23:28
5F：→ airslas2012 :这样还有关？ 04/14 23:29
6F：推 ss1132 :对 04/14 23:29
7F：→ airslas2012 :okay 那 cos^2/sin^2 有什麽积分方法比较好? 04/14 23:30
8F：推 ss1132 :还记得cotx的微分吗? 04/14 23:33
9F：→ ss1132 :可以直接用... 04/14 23:33
10F：→ airslas2012 :ln sin 我用用看 感谢~ 04/14 23:33
11F：→ airslas2012 :囧技成积分的去了 04/14 23:35
12F：→ airslas2012 :cotx的微分我会阿，我想把csc^2推回去cotx ~ 04/14 23:35
14F：→ airslas2012 :这样应该没错了吧?! 04/14 23:55
15F：推 ss1132 :可以在c/(s^2) ds的时候就用分部积分 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