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![[Post New]](/templates/default/images/icon_minipost_new.gif) 16 Feb 2008 16:22:52 IST
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Hey....guyz I think most of 12th std students will have difficulty in integration. So letz start a game...,a game in integration. I will give a problem in integration. Those who solve it should write another problem and so on. *Those who submit problems should try to give standard problems. (*)And finally we can decide who is the king in Integration........................
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16 Feb 2008 16:27:41 IST
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Integrate sin^2(x) dx/(cosx+sinx) *limits given 0 to pi/2 So......on your mark...set.... go
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17 Feb 2008 11:39:07 IST
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I = sin^2(X) dx / (sinx + cosx)
use the property...
I = cos^2(X) dx / (sinx +cosx)
then add them..:
2I = dx / (sinx + cosx)
then mult. n div. by root 2 in denomeinator and then solve it...
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17 Feb 2008 11:40:12 IST
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now my question...
1) integrate e^1/x dx
or
2) integrate e^x.logx dx
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17 Feb 2008 12:51:44 IST
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One more thing......If U think that the method of solution for the problem that you have posted is different from that of the answered,U can explain ur own method.....Letz master in integration..........
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17 Feb 2008 12:59:44 IST
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So.... My method of solving the problem that I have posted is after getting 1/sinx+cosx Put t = tan x/2 then..., dx=2dt/1+t^2 sinx=2t/1+t^2 cosx=1-t^2/1+t^2 Substitue...and integrate using any standerd formula Hope u got it
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17 Feb 2008 13:00:48 IST
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Now proceed with ankit7465's Problem................
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17 Feb 2008 13:19:49 IST
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You can rate those who give the perfect answer....I have rated you..ankit7465
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17 Feb 2008 15:02:06 IST
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ankit both r non-integrable my question--- (sin -1 x - cos -1x)/ (sin -1x + cos -1x) dis is ncert question no. 19 misc ex(pg 352)
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18 Feb 2008 15:51:47 IST
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.
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19 Feb 2008 18:44:00 IST
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wat was blank post for?
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19 Feb 2008 19:04:37 IST
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for the previous question denominator is  /2 so take 2/ common cos -1x= /2-sin -1x so we get numerator in terms of sin-1x put x=t and hence the problem |
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19 Feb 2008 19:32:54 IST
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Find 0 /2 sin2(sinx) + cos2(cosx) dx
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Time wounds all heels |
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19 Feb 2008 20:00:05 IST
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split it into 2 integrals as I and J
for I that is sin^ 2 (sinx)
apply property 4
u get I as sin^2 (cosx)
now add new I and old J
so pi/2
correct me if i m wrong
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