The value of $\int\limits_{-1}^{1} |x| \, dx$ is:

1

The correct answer is Option (3) → 1

$\int\limits_{-1}^{1} |x| \, dx = \int\limits_{-1}^{0} -x \, dx + \int\limits_{0}^{1} x \, dx$

$= -\left[ \frac{x^2}{2} \right]_{-1}^{0} + \left[ \frac{x^2}{2} \right]_{0}^{1}$

$= -\left[ \frac{(0)^2}{2} - \frac{(-1)^2}{2} \right] + \left[ \frac{(1)^2}{2} - \frac{(0)^2}{2} \right]$

$= -\left[ 0 - \frac{1}{2} \right] + \left[ \frac{1}{2} - 0 \right]$

$= \frac{1}{2} + \frac{1}{2} = 1$