Question

Evaluate ${\int }_{-2}^3\frac{dx}{x^3}$

• A. $0$
• B. $-\frac{5}{72}$
• C. $\frac{5}{72}$
• D. None of these

Answer 1

The correct option is C $\frac{5}{72}$

${\int }_{-2}^3\frac{dx}{x^3}$ $={\int }_{-2}^2\frac{dx}{x^3}+{\int }_2^3\frac{dx}{x^3}$

$=0+{\int }_2^3{x}^{-3}dx={\left[\frac{1}{-2x^2}\right]}_2^3=\frac{1}{8}-\frac{1}{18}=\frac{5}{72}$

Note: $\frac{1}{x^3}$ is an odd function