Calculus: Early Transcendentals 9th Edition

Published by Cengage Learning
ISBN 10: 1337613924
ISBN 13: 978-1-33761-392-7

Chapter 5 - Section 5.3 - The Fundamental Theorem of Calculus - 5.3 Exercises - Page 407: 60

Answer

$\int_{1}^{6} x^{-4}~dx = \frac{215}{648}$

Work Step by Step

We can find the area under the graph: $\int_{1}^{6} x^{-4}~dx$ $=-\frac{1}{3}x^{-3}~\vert_{1}^{6}$ $=-\frac{1}{3}(\frac{1}{6^3} -\frac{1}{1^3})$ $=-\frac{1}{3}(\frac{1}{216} -1)$ $=-\frac{1}{3}(-\frac{215}{216})$ $=\frac{215}{648}$
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