Evaluate $\int\limits_{-1}^{2} \frac{|x|}{x} dx$.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 1
Let $I = \int\limits_{-1}^{2} \frac{|x|}{x} dx$.
Since $\frac{|x|}{x} = \begin{cases} \frac{-x}{x}, & x < 0 \\ \frac{x}{x}, & x > 0 \end{cases}$
$= \begin{cases} -1, & x < 0 \\ 1, & x > 0 \end{cases}$
$∴I = \int\limits_{-1}^{0} (-1) dx + \int_{0}^{2} (1) dx$
$I = [-x]_{-1}^{0} + [x]_{0}^{2}$
$I = [0 - (-(-1))] + [2 - 0]$
$I = -1 + 2 = 1$