IIT JEE , AIEEE Forum - Mathematics , Integral Calculus

Sree

Is this correct?

Let I=

(1/x) dx

using uv method :

u=1/x and dv=dx

so du= (-1/x²) dx and v=x

I=(1/x ) * ( x) -

( -1/x²) * (x) dx

I=1-

(-1/x) dx

I=1+

(1/x) dx

But I=

(1/x)dx

I= 1 + I

Therefore 0=1

hash_include

obviously it is wrong..
you are not accounting for the fact that this is indefinite integration..
so the constants of integration will differ..

it should be
I₁= 1 + I₂

uday_zingtudor

Hey man!!

check this out

can u find the mistake in this??

write x+x+x+x+x+x+....... upto x times = x^2

differentiating on both sides

1+1+1+1+1+1+1+ ....x times = 2x

x=2x

that implies 1=2

Can u find the mistake ????

This is a CHALLENGE !!!

computer001

x+x+x....x times=x^2 valid only for integers
and a function taking only integral values is not continuous...hence it aint differentiable...hence u r wrong

hash_include

uday.. writing
x + x+ x +... x times = x^2
is possible only for natural numbers..
so the function is discontinuous..
hence, you cant differentiate..

uday_zingtudor

yeah u ppl are right

I thought no one could answer

neeraj_agarwal_1990

everybody on goiit may be knowing it...has been discussed 100's of times...many solutions...many mistakes :)

puneet

hii

lets discuss thngs whch make sense .. lets not waste time .. JEE is round the corner all of u shud preprae hard ..

cheers

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