Question

integration of greatest integer of logx

Answer 1

split from 1 to e and e to e^2

from 1 to e [lnx] has value= 0 in range 0 to 1

as ln 1= 0

and ln e = 1


from e to e^2, [ln x] has value 1 as lne = 1

and ln e^2 = 2

As we know upper limit is not included

so less than 2 , So greatest integer becomes 1

S0 0 + e^2 - 1

e^2 -1

(2) is correct