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: 92

Answer

\[ = \frac{1}{{{s^2}}}\]

Work Step by Step

\[\begin{gathered} f\,\left( t \right) = t\,\,\,\,\, \to \,\,\,\,f\,\left( s \right) = \frac{1}{{{s^2}}} \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ \mathcal{L}\,\,\,\left[ t \right]\left. { = \frac{{ - t{e^{ - st}}}}{s}} \right|_0^\infty + \frac{1}{s}\int_0^x {{e^{ - st}}dt} \hfill \\ \hfill \\ integrate\,\,and\,\,evaluate \hfill \\ \hfill \\ = \frac{1}{s}\mathcal{L}\,\,\,\left[ t \right] = \frac{1}{s}\,\left( {\frac{1}{s}} \right) \hfill \\ \hfill \\ solution \hfill \\ \hfill \\ = \frac{1}{{{s^2}}} \hfill \\ \end{gathered} \]
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.