Calculus: Early Transcendentals 8th Edition

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

Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises: 13

Answer

$$h'(x) = xe^x$$

Work Step by Step

$$h(x) = \int\limits^{e^x}_1 {ln(t)dt}$$ Using FTC 1, substitue in the upper bound for t and multiply by the derivative of the upper bound. $$h'(x) = ln(e^x) \times (e^x)'$$ Simplify. [Note that $ln(e^x) = x$] $$h'(x) = xe^x$$
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