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