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: 85

Answer

\[P = 20000\]

Work Step by Step

\[\begin{gathered} P = 0.00005\int_0^\infty {t{e^{ - 0.00005t}}dt} \hfill \\ \hfill \\ integrate\,\,\,by\,\,parts \hfill \\ \hfill \\ P = 0.00005\,\,\,\mathop {\lim }\limits_{b \to \infty } \,\,\,\left[ {t\,\left( {\frac{{{e^{ - 0.00005t}}}}{{ - 0.00005}}} \right) - \,\,\,\left( {\frac{{{e^{ - 0.00005t}}}}{{ - {{0.00005}^2}}}} \right)} \right]_0^b \hfill \\ \hfill \\ use\,\,the\,\,ftc \hfill \\ \hfill \\ P = 0.00005\,\,\,\mathop {\lim }\limits_{b \to \infty } \,\,\,\,\left[ {b\,\left( {\frac{{{e^{ - 0.00005b}}}}{{ - 0.00005}}} \right) - \,\left( {\frac{{{e^{ - 0.00005b}}}}{{ - {{0.00005}^2}}}} \right) + \frac{1}{{ - {{0.00005}^2}}}} \right]\, \hfill \\ \hfill \\ {\text{evaluate}}\,\,{\text{the}}\,\,{\text{limit}} \hfill \\ \hfill \\ P = \frac{1}{{0.00005}} \hfill \\ \hfill \\ or \hfill \\ \hfill \\ P = 20000 \hfill \\ \hfill \\ \end{gathered} \]
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