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: 41

Answer

\[ - \frac{3}{8}\]

Work Step by Step

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