Answer
\[ = \,10\]
Work Step by Step
\[\begin{gathered}
Velocity\,\,of\,\,an\,\,object\,\,is\,\,given\,\,by \hfill \\
\hfill \\
v\,\left( t \right) = \frac{{10}}{{\,{{\left( {1 + t} \right)}^2}}} \hfill \\
\hfill \\
\,find\,\,the\,\,maximum\,\,distance\,\,the\,\,object \hfill \\
\hfill \\
s\,\left( t \right) = \int_0^\infty {\frac{{10}}{{\,{{\left( {1 + t} \right)}^2}}}} \,dt \hfill \\
\hfill \\
{\text{integrate}}\,\,{\text{using}}\,\,{\text{the}}\,\,{\text{definiton}}\,\,{\text{of}}\,\,{\text{improper}}\,\,\,{\text{integrals}} \hfill \\
\hfill \\
s\,\left( t \right) = \mathop {\lim }\limits_{b \to \infty } \,\,\left[ { - \frac{{10}}{{1 + t}}} \right]_0^b \hfill \\
\hfill \\
use\,\,the\,\,ftc \hfill \\
\hfill \\
s\,\left( t \right) = \mathop {\lim }\limits_{b \to \infty } \,\,\left[ { - \frac{{10}}{{1 + b}}\, + \,10} \right] \hfill \\
\hfill \\
evaluate\,\,the\,\,\lim it \hfill \\
\hfill \\
s\,\left( t \right) = 0 + 10\, = \,10 \hfill \\
\hfill \\
then \hfill \\
\,\,the\,\,maximum\,\,distance\,\,that\,\,object\,\,can \hfill \\
travel\,\,is\,\,10\,\,miles. \hfill \\
\hfill \\
\end{gathered} \]
