Question

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

Answer 1

Let $I={\int }_2^3\frac{1}{x}dx$
$\Rightarrow \int \frac{1}{x}dx=\log |x|=F\left(x\right)$
By second fundamental theorem of calculus, we obtain
$I=F\left(3\right)-F\left(2\right)$
$=\log |3|-\log |2|=\log \frac{3}{2}$