Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 5 - Integration - 5.3 Fundamental Theorem of Calculus - 5.3 Exercises: 37

Answer

\[ - \frac{5}{2}\]

Work Step by Step

\[\begin{gathered} \int_{1/2}^1 {\left( {{x^{ - 3}} - 8} \right)} dx \hfill \\ \hfill \\ {\text{Integrate using }}\int {{x^n}dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C} \hfill \\ \hfill \\ = \left[ {\frac{{{x^{ - 2}}}}{{ - 2}} - 8x} \right]_{1/2}^1 \hfill \\ \hfill \\ Therefore \hfill \\ \hfill \\ = \left[ { - \frac{1}{{2{x^2}}} - 8x} \right]_{1/2}^1 \hfill \\ \hfill \\ {\text{Use the fundamental theorem of calculus}} \hfill \\ \hfill \\ = \left[ { - \frac{1}{{2{{\left( 1 \right)}^2}}} - 8\left( 1 \right)} \right] - \left[ { - \frac{1}{{2{{\left( {1/2} \right)}^2}}} - 8\left( {1/2} \right)} \right] \hfill \\ \hfill \\ {\text{Simplify}} \hfill \\ \hfill \\ \left( { - \frac{{17}}{2}} \right) - \left( { - 6} \right) \hfill \\ \hfill \\ - \frac{5}{2} \hfill \\ \hfill \\ \end{gathered} \]
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