Question

Evaluate the definite integral:
${\int }_2^3\frac{1}{x}.dx$

Answer 1

${\int }_2^3\frac{1}{x}.dx$

Let,

$F\left(x\right)=\int \frac{1}{x}dx=\log |x|$

Hence

${\int }_2^3\frac{1}{x}.dx=F\left(3\right)-F\left(2\right)$

$=\log |3|-\log |2|$

$=\log \left|\frac{3}{2}\right|$

$=\log \frac{3}{2}$