Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 5 - Section 5.2 - The Definite Integral - 5.2 Exercises - Page 390: 45

Answer

$\int_{1}^{3}e^{x+2}~dx = e^5-e^3$

Work Step by Step

We can evaluate the integral using properties of integrals: $\int_{1}^{3}e^{x+2}~dx$ $= \int_{1}^{3}e^x\cdot e^2~dx$ $= e^2\int_{1}^{3}e^x~dx$ $= e^2(e^3-e)$ $= e^5-e^3$
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