Answer
$\int_{-3}^{-2}\dfrac{dx}{x}=\ln(\dfrac{2}{3})$
Work Step by Step
Solve $\int_{-3}^{-2}\dfrac{dx}{x}$
$\int_{-3}^{-2}\dfrac{dx}{x}=[\ln |x|]_{-3}^{-2}$
This implies $[\ln |x|]_{-3}^{-2}=\ln |-2|-\ln |-3|$
$=\ln 2-\ln 3$
Use logarithmic properties, $\ln m-\ln n=\ln(\dfrac{m}{n})$, we have
Hence, $\int_{-3}^{-2}\dfrac{dx}{x}=\ln(\dfrac{2}{3})$