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Integral Calculus

Scorching goIITian

Joined:	25 Oct 2007
Post:	226

2 Nov 2007 12:51:23 IST

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683

integratn problem

None

(cot ^-1 ( e^x) )/ ( e^x) dx

options :-

(1) 1/2 ln ( e^2x+ 1) - (cot ^-1 ( e^x) )/ ( e^x) + x+ C

(2) 1/2 ln ( e^2x+ 1) + (cot ^-1 ( e^x) )/ ( e^x) + x+ C

(3) 1/2 ln ( e^2x+ 1) - (cot ^-1 ( e^x) )/ ( e^x) - x+ C

(4) 1/2 ln ( e^2x+ 1) + (cot ^-1 ( e^x) )/ ( e^x) - x+ C

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Comments (8)

'',' Off to a nu start!!

Blazing goIITian

Joined: 13 Jan 2007

Posts: 1289

2 Nov 2007 17:21:06 IST

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DIFFERENTIATE THE OPTIONS ..... WATEVER OPTION THAT WILL GET THE QN. WILL BE THE RIGHT ANSWER......

HOPE U GET IT><

MoNaLisA :):):)

Scorching goIITian

Joined: 25 Oct 2007

Posts: 226

2 Nov 2007 21:41:01 IST

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but hw do v solve it !!!!!!!

aditi garg

Scorching goIITian

Joined: 2 Nov 2007

Posts: 288

2 Nov 2007 22:09:45 IST

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see its very simple....just multiply and divide the given expression by e^x and thn put e^x as t.... the expression becomes... cot ^ -1 t/t^2 dt

thn apply that by parts formula of integration and u can easily get the answer... option 3 is correct....and 1 piece of advice at the first attempt nvr try to solve any integration prob by differentiating the options... its just a waste of time... u can use it in case ur sitting for an examination and not getting any answer

pradnya pednekar

New kid on the Block

Joined: 24 Oct 2007

Posts: 8

6 Nov 2007 20:58:37 IST

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put e^x=t
x=logt
dx=dt/ t
int becomes--cot^-1t/ t^2 dt

'',' Off to a nu start!!

Blazing goIITian

Joined: 13 Jan 2007

Posts: 1289

6 Nov 2007 21:03:29 IST

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when u hv options den why to do it properly...sum qns. are meant to be done by done by these methods..

astrojith

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Joined: 5 Jun 2007

Posts: 336

8 Nov 2007 21:02:29 IST

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Shubham, its not easy to differentiate these. And what if the answer is the 4th one ? You'll lose a lot of time.

And yo mona, is that you in the picture ?

richa sharma

Cool goIITian

Joined: 7 Nov 2007

Posts: 91

8 Nov 2007 21:04:52 IST

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yeah...differentiating every expression would be a real waste of time!!

Aditya Arora

Blazing goIITian

Joined: 3 Dec 2006

Posts: 1043

8 Nov 2007 21:14:02 IST

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Hi,

Look,

(cot ^-1 ( e^x) )/ ( e^x) dx

(cot ^-1 ( e^x) )*e^x/ ( e^2x) dx ------------------ 1

Put t = e^x ------------------- 2

dt = e^x dx --------------------- 3

cot ^-1 (t) / ( t²) dx

Now, apply product rule by taking cot^-1(t) as first function and t² as second function.

After that you should be able to solve this ques.

Hope u got it !!!!!!

Do tell me in case of problems !!!!

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