Answer
$1000$
Work Step by Step
Consider $f(r)=\int_{0}^{1} \dfrac{1}{r^{0.999}} dr$
$\lim\limits_{a \to 0^{+}} f(r)= \lim\limits_{a \to 0^{+}}\int_{0}^{1} \dfrac{1}{r^{0.999}} dr=\lim\limits_{a \to 0^{+}} [\dfrac{r^{0.001}}{0.001}]_{1}^{a}$
or, $\lim\limits_{a \to 0^{+}} [1000-1000a^{-0.001}]= 1000$
