# How do you test the improper integral int x^-0.9 dx from [0,1] and evaluate if possible?

Aug 16, 2017

${\int}_{0}^{1} {x}^{- 0.9} \mathrm{dx} = {\lim}_{a \rightarrow {0}^{+}} {\int}_{a}^{1} {x}^{- 0.9} \mathrm{dx}$
$= {\lim}_{a \rightarrow {0}^{+}} {\left[10 {x}^{0.1}\right]}_{a}^{1}$
$= 10 - {\lim}_{a \rightarrow {0}^{+}} 10 {a}^{0.1}$
$= 10$