1) If f(x) = x1+((log x)(log x)(log x)(log x).....\propto). for all values of x \epsilon
[1 ,\propto) ; then \int_{1}^{2e}{f(x)dx} is equal to :
a)e2 - 12
b)e2 + 12
c) e2 - 2e2
d) none of these
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(the ans given is a)
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3 Answers
62This one is more a googley i guess
if log x is greater than 1, the function is zero..
If log x is less than 1, the function is x
So the integral is indeed a
11@ nishant bhayia
they have broken the (log x)(log x)(log x)(log x)....
in this way....
(log x)(log x)(log x)..... { ( ---> 0 ) for 1<x<e
{1 for x=e
{ (---> infinity) for x>e
how can they say the first break up.....
suhd'nt it be tending to minus infinity..??
29@Sandipan..
Anything < 1 ..multiplied infinite times will yield 0..
and anything > 1 multiplied by infinite times yield ∞...
since logx < 1 ..when x ε ( 1,e)
and logx > 1 when x ε (e , ∞ )