Correct Answer - Option 3 : 2
Concept:
\(\rm \int_{a}^{c} \left | x \right |dx\) = \(\rm \int_{a}^{b} -x dx + \int_{b}^{c} x dx\)
Calculation:
|x| = \(\rm \begin{cases} \rm x & \text{ if } \rm x\geq 0 \\\rm -x & \text{ if } \rm x < 0 \end{cases}\)
Let I = \(\rm \int_{0}^{2} \left | x \right |dx\)
= \(\rm \int_{0}^{2} xdx\)
\(= \rm \left [\frac{x^{2}}{2} \right ]_{0}^{2}\)
= \( \rm \frac{1}{2}[(2)^2 - (0)^2] \)
= 2
