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: 7


$10^4e^{0.0004 }$.

Work Step by Step

$$\int_{-\infty}^4e^{0.0001t}dt=\lim\limits_{R \to- \infty}\int_ R^4e^{0.0001t}dt \\=\lim\limits_{R \to -\infty} \frac{1}{0.0001}e^{0.0001t}|_R^4=\frac{1}{0.0001}\lim\limits_{R \to- \infty}(e^{0.0004 }-e^{0.0001R})=\frac{1}{0.0001}e^{0.0004 }.$$ Then the integral converges and its value is $10^4e^{0.0004 }$.
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