what is the relationship between lnx and 1xSolutionThe relat

what is the relationship between lnx and 1/x?

Solution

The relation between ln x and (1/x) is explained in terms of definite and indefinte integrals.

Indefinite integral:

Int (1/x) dx + C = lnx +C.

Definite integral:

{Int (1/t) dt from t = 0 to t = x} = lnx.

Or in other words ln (x) is the area under the curve f(x) = ln(t) between the ordinates t= 0 to t = x, which could be calculated by evaluation of the definite integral Int (1/t)dt from t = 0 to t =x.