Science:Math Exam Resources/Courses/MATH105/April 2018/Question 01 (g)/Solution 1

Using the power rule, we get

$$\int _{-3}^{-1}x^{-3}\,dx=\left[-{\frac {1}{2}}x^{-2}\right]_{-3}^{-1}=-{\frac {1}{2}}+{\frac {1}{18}}=-{\frac {4}{9}}.$$

Answer: $\color {blue}-{\frac {4}{9}}.$