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Integral Calculus

Blazing goIITian

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9 Mar 2009 13:17:12 IST

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417

GMP 1 -

None

The number of possible continuous f(x) defined in [0, 1] for which

I₁ = = 1,

I₂ = = a,

I₃ = = a²

is ???

options are 0, 1, 2, infinite ....

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Comments (8)

Mirka

Blazing goIITian

Joined: 13 Aug 2008

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9 Mar 2009 13:40:23 IST

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Answer was given as 1 ....

kishore subramanian

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10 Mar 2009 01:46:53 IST

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Hence from the three results we can see that

Hence we can say that the value of I depends only on x and not on f(x)....Hence the number of functions of f(x) has to be one..

shilpa nair

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10 Mar 2009 14:54:22 IST

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@above...in I2...u hav changed x to 1-x but u forgot to change f(x) = f(1-x)!!

Ankit

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10 Mar 2009 15:01:27 IST

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in I3 too

saharsha kumar keshkar

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10 Mar 2009 16:52:07 IST

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ya i think answer 1.

KAPIL CVS

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11 Mar 2009 10:09:52 IST

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SAHARSHA ,

PLS XPLAIN HOW U GOT IT.

Mirka

Blazing goIITian

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Posts: 1313

11 Mar 2009 14:22:41 IST

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Hi guys, this Qsn has been solved here & ans supposed 2 b zero –

http://targetiit.com/iit_jee_forum/posts/integration_3164.html

shilpa nair

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Posts: 239

11 Mar 2009 19:36:38 IST

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yup...i was gettin 0 as the answer...dats y didn't postd..thanxx for confirmin it!!

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