# What is the net area between f(x)=ln(2/x) in x in[1,2]  and the x-axis?

Jan 15, 2016

$1 - \ln 2$

#### Explanation:

Using the identity

$\ln \left(\frac{a}{b}\right) \equiv \ln a - \ln b$,

we can write $f \left(x\right) = \ln 2 - \ln x$.

The area is represented by the following integral.

${\int}_{1}^{2} \left(\ln 2 - \ln x\right) \mathrm{dx} = {\left[\left(\ln 2 + 1\right) x - x \ln x\right]}_{1}^{2}$

$= 1 - \ln 2$