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Integral Calculus

New kid on the Block

 Joined: 8 Nov 2006 Post: 3
10 Nov 2006 19:26:36 IST
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24
2356
indefinate int.
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Integral Calculus

1/(cos3x - sin3x)

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Cool goIITian

Joined: 29 Oct 2006
Posts: 43
10 Nov 2006 23:14:03 IST
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hiii
U have put the topic as definiite integral. Have u forgotten to put the limits of integration??? I am finding it difficult to solve it otherwise.

Forum Expert
Joined: 6 Nov 2006
Posts: 22
11 Nov 2006 17:39:45 IST
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dear rohit,

please provide the limits to help us solve the query.

thanks

Cool goIITian

Joined: 26 Oct 2006
Posts: 68
12 Nov 2006 11:07:48 IST
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[0 ][/2] log(tan x + cos x) =

Cool goIITian

Joined: 29 Oct 2006
Posts: 43
12 Nov 2006 11:13:35 IST
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Yaar r u sure about the question.......... i am getting no hint at all .. what is the answer any idea ??? Is the question absolutely correct ??

Cool goIITian

Joined: 26 Oct 2006
Posts: 68
12 Nov 2006 11:16:02 IST
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I'm sure abt the question and I don't know what the answer is. I've been trying this q for quite a while without much success.

Cool goIITian

Joined: 29 Oct 2006
Posts: 43
12 Nov 2006 11:18:17 IST
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See when we are using the trick of putting /2 - x instead of x .... I think we should get some form where we eliminate the quantity in the log by adding to the original integral .. and this is not working here .. I think something wrong with the question itself .... !!!

Cool goIITian

Joined: 26 Oct 2006
Posts: 68
12 Nov 2006 11:20:23 IST
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You can be sure the q is right. Try solving it.

Cool goIITian

Joined: 29 Oct 2006
Posts: 43
12 Nov 2006 11:20:58 IST
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k ..... let us see

Cool goIITian

Joined: 29 Oct 2006
Posts: 43
12 Nov 2006 11:26:16 IST
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I am giving up ........ no idea at all ... telll me if u find some solution

Joined: 19 Oct 2006
Posts: 1558
12 Nov 2006 12:16:54 IST
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Dear Lois, please post new queries as a separate question, if the discussion needs expert's advice.

Best,

Forum Expert
Joined: 12 Nov 2006
Posts: 25
12 Nov 2006 19:48:23 IST
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[0 ][ /2]log (tan x + cos x) is non-integrable.

Are you sure that you typed the correct problem? The correct question would be

[0 ][ /2]log (tan x + cot x)

Cool goIITian

Joined: 29 Oct 2006
Posts: 43
12 Nov 2006 22:53:25 IST
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Now this makes some sense .......... people be sure you do type correct questions ...

New kid on the Block

Joined: 4 Nov 2006
Posts: 3
14 Nov 2006 10:55:58 IST
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Hi ,arey yaar i think that u shud try foll .steps:
1)sepr8 deno.
2) put cosx as 1-t^2/1+t^2 & sinx as 2t/1+t^2 .
where t-> tan(x/2)

P.N : I TRIED this 1 on 3pgs B4 Being fed up. fromm next time do provide ans. & yEs LIMITS.
FROM WHERE DID U GeT THi\$ Qn.

Cool goIITian

Joined: 26 Oct 2006
Posts: 68
26 Nov 2006 23:34:52 IST
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Hi all,

I'm damn sure the problem is right. puneet1622 I haven't posted it wrong. A friend of mine (cleared JEE 2006) gave me this prob with a warning that everyone will tell me it is non-integrable but it is. Sadly, he didn't give me the answer can you help me get to the answer?

Cheers,
Lois

Joined: 19 Oct 2006
Posts: 1558
27 Nov 2006 00:16:14 IST
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Hmmm....

this is interesting... finally we have something that challenges everyone! . The team who has tried to solve this one is one of the best in the country and everyone is on consensus on this one. Lois, why dont you try and get the answer for this one. If you can figure out the solution from your friend and the post it here then goIIT sends you a free goodie ! how about that?

cheers

Blazing goIITian

Joined: 16 Mar 2007
Posts: 838
20 Jun 2007 18:02:07 IST
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Hey man if you don't put the limits then the function's integral takes inverse hyperbolic functional slope . Anyways, this is the answer :-
(2/3)  [ tan-1 (cos x + sinx ) + 2 tanh-1 ( ( tan (x/2) +1 ) / 2 ) ]

Blazing goIITian

Joined: 16 Mar 2007
Posts: 838
20 Jun 2007 18:11:55 IST
1 people liked this

And by th way , the one asked by Lois involves polylogarithmic function
and natural logarithmic variables whose properties I don't remember at this moment.

Blazing goIITian

Joined: 16 Mar 2007
Posts: 838
20 Jun 2007 18:32:55 IST
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Hey I have tried ...it may be correct just tell me otherwise I will have to revise the logarithmic properties.Well it is has to be integrated with reference to complex plane
because ln z = ln |z| +i arg (z) where is z is a complex number.
(1/2) i ( ( x2+ polylog (2 , e 2ix )  )  where i = -1

Blazing goIITian

Joined: 16 Mar 2007
Posts: 838
20 Jun 2007 19:11:35 IST
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Oh my god !..................I just forgot to tell that .....I hate to ask for this.....but please rate .

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