Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 7 - Integration Techniques - 7.8 Improper Integrals - 7.8 Exercises: 59

Answer

\[ = \,10\]

Work Step by Step

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