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 441: 51


The integral converges to: $\dfrac{-1}{a}; a \lt 0$

Work Step by Step

We will compute the integral as follows: $\int_{0}^{\infty} e^{ax} \ dx= \lim\limits_{R \to \infty} \int_{0}^R e^{ax} \ dx \\=\lim\limits_{R \to \infty} \dfrac{e^{ax}}{a}|_0^R \\=\lim\limits_{R \to \infty} [\dfrac{e^{aR}}{a}-\dfrac{1}{a}]\\=0-\dfrac{1}{a}\\=-\dfrac{1}{a}$ Hence, the integral converges to: $\int_{0}^{\infty} e^{ax} \ dx =\dfrac{-1}{a}; a \lt 0$
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.