S!UwlnG 發表於 12-3-2009 20:40:30

One question about integration

Find the following. (please do not use the method of substitution)
Thanks a lot.

-終場ソ使者- 發表於 12-3-2009 20:51:17

=1/2∫1/(1+cos2x)d(2x)
=1/2．ln(1+cos2x)+C
有d怪- -

無．話可說 發表於 12-3-2009 20:56:13

本帖最後由 無．話可說 於 12-3-2009 21:06 編輯

#2 你錯了 haa
please do not use the method of substitution -.-

諗到啦..
ans 係 1/2 tanx + c

先用 1+ cos2x = 2cos^2 x
then change it to sec^2 x

-終場ソ使者- 發表於 12-3-2009 21:22:43

係喎
trigonometric個d唔係好熟@@
但我個題錯左邊(如果可以用substitution)

無．話可說 發表於 12-3-2009 21:38:36

如果係 1/2∫1/(1+cos2x)d(1+cos2x)
你就ok
但係因為你係d(2x) 而唔係 d(1+cos2x)

S!UwlnG 發表於 12-3-2009 21:41:58

3# 無．話可說
really appriciate
this is the question no.1 in section A in my mock
i just left it blank:L
fortunately, it carries 2 marks only:)

Zend 發表於 12-3-2009 23:00:44

sometimes u need to change it..
cos2x = 2cos^2x-1 ..
sec^2x is good
都係果句,數學都係要背-.-
要做數學家慢慢推先白痴

無．話可說 發表於 12-3-2009 23:42:10

sometimes u need to change it..
cos2x = 2cos^2x-1 ..
sec^2x is good
都係果句,數學都係要背-.-
要做數學家慢慢推先白痴
Zend 發表於 12-3-2009 23:00 http://nakuz.com/bbs/images/common/back.gif
呢句好有味道 a_a

Zend 發表於 13-3-2009 08:00:05

我都想知可唔可以推到
by definition

-終場ソ使者- 發表於 13-3-2009 19:05:21

推唔到就唔會有呢條formula- -
人地為左方便,會直椄忽略d step去記個ans
不過我覺得應該要睇下個證明
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