Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 33

Answer

The integral diverges.

Work Step by Step

We have $$ \int_{1}^{\infty} \frac{e^{\sqrt{x}} d x}{\sqrt{x}}=2\int_{1}^{\infty} e^{\sqrt{x}} d {(\sqrt{x})}=2e^{\sqrt{x}}|_{1}^{\infty} =2(\infty-e)=\infty. $$ Hence, the integral diverges.
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.